CHC5028 Software Development withC/C++CourseworkImportant DatesWeek 10 (an available day in that week): Class test.Week 12 (16/12/2024-20/12/2024): Project demonstration and viva assessment. Source codes file submission.Background“Text adventures”, now called “interactive fiction”, were among the first type of computergame ever produced. These games have no graphics; the player reads the story of thegame in text, and decides what their character will do by typing commands at a prompt.Although less popular now, text adventures are still played and created, and developedinto the original online RPGs (MUDs). You can play some sample modern textadventures here:Discworld MUD, BatMUD, These are playable online via a web browser. It is advisable to try out the games to getan understanding of how the games behave.For this coursework, you will be creating a simple game engine for a text adventure.You are not required to write an actual adventure, only the back-end program code thatwould support one. You will need to add some material to the program in order to test it,but this may just be simple test material. You may add interesting descriptions or storiesto your program if you want to, but there are no marks for doing so.You are provided with a CLion project containing a very simple game harness whichsupports only two commands: going north (north or n), and quitting (quit). Extend itby doing the exercises below. Note that the later exercises are less explicitly describedthan the earlier ones, meaning that you must solve more problems yourself. This isintentional.The coursework is written to be built using gcc through CMake and CLion. It is notrecommended that you attempt to build it using Visual Studio or XCode.Important: If you are building the sample coursework on a platform other than Windows, or on a machine which does not have the Windows API installed, you may get an error in thefile wordwrap.c. This file calls a Windows specific function to find thewidth of the console. If you get this error, remove the #include fromthe top of the file, and editthe initWordWrap() function by deleting its contents andreplacing them with consoleWidth = 80; currentConsoleOffset = 0;. You can change 80 here to anynumber that makes the output comfortably readable.Task 1 (10% of the mark)In the current system, you can only move North. Extend the engine to allow movement inallfour compass directions.• Add properties to the Room class for storing east, south, and west exits. Theseproperties will need accessor methods.• Add code to the gameLoop method to understand the commands east, south, andwest (and the abbreviations e, s and w) and to handle them in a similar way to north.• Modify initRooms to create more rooms using the new exits to test yourcode.• The rooms created should be constructed in a reasonable and logical relationship that makes the game playable and sensible.Task 2 (15% of the mark)A key part of most text adventure games is the ability to move objects around. Objects can be found in rooms and can be picked up and put down by the player. Add this capability to the game engine.• Create a GameObject super class. It should contain at least a weight, and akeyword (for the player to use when typing commands).• Modify the Room class so that each Room includes a list of GameObjects in theroom.• Create a derived class Weapon of GameOjbect class, the weight of each object of Weapon should be limited in a range of 5-10. It should contain a property named harm which should be limited in a range of 10-30. • Create a derived class Food of GameObject class, the weight of each object of Foodshould be limited in a range of 1-5. It should contain a property named energy which should be limited in a range of 1-10. • Modify initRooms to create some GameObjects ((including food and weapon objects)and put them in the rooms. Use this to test your program. (No marks are assigned specifically for this task, but without it, the ones following cannot be demonstrated.)Task 3 (15% of the mark)A key part of most text adventure games is the ability to fight with the NPC enemy. The NPC can be found in rooms and the player can fight with them. Add this capability to the game engine.• Create a pure virtual EnemyObject class. It should contain at least a health, and a keyword (for the player to use when typing commands). It should contain a virtual method damage().• Modify the Room class so that each Room includes a list of EnemyObject in theroom.• Create a derived class Boss of EnemyObject class, the health of each object of Boss should be 100.• Create a derived class Clowns of EnemyObject class, the health of each object of Clowns should be 30.• Modify initRooms to create some EnemyObjects ((including boss and clowns objects) and put them in the rooms. Use this to test your program. (No marks are assigned specifically for this task, but without it, the ones following cannot bedemonstrated.)• You need to consider different reasonable damage value for each different enemy objects’ damage() method.Task 4 (5% of the mark)• Modify the State class to include a representation of the player’s physical strength,called strength, which is initiated as 100, and when strength goes to 0, the program shall be terminated. • Modify the Room::describe() method to print out the keywords of all theobjects in the room, formatted as nicely as possible.Task 5 (30% of the mark)• Modify the gameLoop method to pay attention to the second word of the commandtheplayer enters, if there is one. The following commands can be used with the second word to search through a) objects in the current room,and b) objects in the inventory, for an object with a keyword matching the second word of the command the player typed. • Implement the player command get which, when typed with an object keyword, willmove that object from the current room list into the inventory. It should display appropriate errors if the object is not in the room, or the object is already in the inventory, or the object does not exist. • Implement the player command drop which, when typed with an object keyword, will move that object from the inventory into the current room list. It should displayappropriate errors if the object is not in the inventory or doesnot exist, etc. (5%)• Implement the player command inventory which will print out the keywords ofall theobjects in the inventory. • Implement the player command eat which, when typed with a food objectkeyword, will print out the player’s strength after adding the energy of the food object to the player’s strength, which should not exceed 100.• Implement the player’s command fight which, when typed with an enemy object keyword if the enemy object exists in the room, will print out the enemy’s health that subtracts from the sum of harm of weapons carried by the player.• The harm is mutual, the player’s strength should reduce the damage of the enemy existing in the room and be printed out. You need to make the damage()in the Boss and Clowns class can be applied when the fight command is working. • You need to make the printout of each command execution demonstrate the explicit status of all objects in the room.Task 6 (25% of the mark)Since most players will not want to play an entire game at one sitting, most games includesave and load (or restore) commands. Implement these commands. Theyshould ask theuser for a filename and then write or read the current game state, to orfrom that file.Note that the layout and descriptions of rooms, and the list and descriptions of objects,are not part of the game state because they do not change during the game. These should not beincluded in the save file and saving them will lose marks.A simple file open, load, and save does not guarantee full marks and may notguarantee“a good mark”.To this end, some important points to consider:• The “game state” may also include the locations of objects the player has dropped inrooms. Would it be a good idea to restructure how object locations are stored?• The “game state” may also include the status of the player and enemy objects. Would it be a good idea to restructure these objects to the original situation?• The State object stores the current room, and objects, using pointers. Pointers cannotsafely be written to disk since addresses may be different when the programis reloaded.How can you enable this data to be safely saved and reloaded?• It is worth ensuring to some degree that the user cannot readily cheat, or spoil the game, by reading or changing a save file. While it is not necessary to implement actual authentication or encryption, at the same time, the file does not have to be just a text dump. This makes it harder to parse when loaded. So, for example, saving the required indexes into a static array of strings may be a better way than saving the strings themselves.Marking scheme for this task:• 5% for basic correct structure of I/O.• 10% for the file format designed for storing the saved game.• 10% for the code that performs the save and the load.Assessment Rules( Very important )Code will be assessed by a demonstration and viva in week 12. You will be asked todemonstrate your code and to explain how it works. There is no hard division of marksbetween code and viva. The marks given are mainly based on your performance in answering the assessor's questions and the accuracy and correctness of the corresponding answers.If you cannot explain your code sufficiently well to satisfy the assessor that it is your own work, they have the right to award 0 marks for that exercise, regardlessof the quality of the code.The fact that your code works does not guarantee full marks. All code is expected to also be readable, maintainable, and efficient. You are not required to exactly follow the stepsin the exercises above. Alternative designs are also acceptable if they can bejustified in the viva. However, designs which substantially reduce efficiency or other desirable properties without corresponding benefits will lose marks.• The deadline for submission of the coursework is Week 12.• In Week 12 you will also be required to demonstrate the final version ofyourwork, and verbal feedback will be given.In addition to final submission and viva in Week 12, there will be two counselling inthe week 10 and week 11 tutorial periods. You also can make appointments with the tutor during the whole semester to Notice on presentation and submissionYou do not need to give a presentation nor submit a report for either section of thecoursework. This coursework’s focus is on the quality of your final code and on your ability tounderstand it, not your software engineering process (which is not expected tobe standard when you are learning the language).Standard rules on plagiarism apply to this coursework.The Code should be your own work and must not be copied from the internet or any other source. If you have difficulty with the coursework, you should approach your practical tutor in the first instance. Posting questions about the coursework on Stack Overflow, Quora, or similar sites may be treated as an incitement to plagiarism. Posting parts of your answer to the coursework on the publicly available internet where other students may access it will be treated asan incitement to plagiarism. Soliciting or obtaining answers to the coursework inexchange for money and any other consideration will be treated as serious academicmisconduct. Asking for coursework answers from any party outside of the University is itselfattempted plagiarism and you should not do it; if that third party commits any of theoffenses in this section on your behalf, you may be held responsible, even if you were not directly aware they would do so (because you should not have asked them in the first place).Assignment DataLearning outcomes See below.Formative deadline Week 10 (2/12/2024-6/12/2024):Coursework Class TestFormative feedback Week 10 (2/12/2024-6/12/2024):CounsellingWeek 11 (9/12/2023-13/12/2023): CounsellingSummative deadline Week 12 (16/12/2024-20/12/2024) Coursework project demonstration and vivaSummative feedback Week 12 (18/12/2023-22/12/2023)Spoken interactive(viva)Final marks after assessment committeesAssignment Weighting Coursework class test 20% of the moduleCoursework project demonstration and viva 30% of the moduleLearning Outcomes• Understand the fundamental concepts of C and C++ programming for objectmanipulation, data structuring and input/output control.• Refine a problem specification into a collection of C++ classes.• Create a software artefact specified in terms of C++ objects and their interrelations.• Research the techniques for safe and efficient programming in C and C++.
Foundations of Applied Mathematics MATH 4700 – Fall 2024 Practice Midterm 1 Perturbation Theory for Finding Roots to Algebraic Equations (20 points) If ϵ is a small positive number (0 < ϵ ≪ 1), construct a good approximation for most negative real-valued root x∗ (in the sense that x∗ < x′∗ for any other real-valued root x’∗) of the equation ϵx3 + 2ϵx2 − 2ϵx + 3 = 0 Your answer should consist of a nonzero main term, the most important nonzero correction term, and an estimate of the error of your approximation. Be sure to fully justify your reasoning. You won’t be penalized if you want to calculate all the roots, so long as you find them correctly, but you won’t get any bonus points either. 2 Perturbation Theory for Finding Roots of Transcendental Equations (20 points plus 10 bonus points) If ϵ is a small positive number (0 < ϵ ≪ 1), construct a good approximation for all order unity real-valued roots to the equation e2+ϵ ln(7+3ϵx) = πx + 8 Your answer should consist of a nonzero main term, the most important nonzero correction term, and an estimate of the error of your approximation. For 10 bonus points give a precise analytical argument for whether or not you expect the equation to have small roots or large roots in addition to the order unity roots you found? Arguments by numerical plots (on the take-home portion) will not by themselves earn much bonus credit. 3 Regular Perturbation Theory for Differential Equations (30 points) If ϵ is a small positive number, construct a good approximation to the solution of the initial value problem: Your answer should consist of a nonzero main term, the most important nonzero correction term, and an estimate of the error of your approximation. 4 Motoring With a Shaky Anchor (40 points plus 20 bonus points) Consider the following mechanical model inspired by a biophysics problem I have been thinking about in my research recently. Figure 1: Schematic of motor moving to the right along a track, attached by a tether to an anchor making small oscillations across the track. A “motor” particle moves along a one-dimensional track while tied by a flexible tether to an anchor, with x(t) denoting the position of the motor along the track, relative to the anchor, as a function of time t. The motor velocity is governed in terms of the along-track force F1(x(t), t) pulling back on it by the following equation: Here v > 0 is the unloaded speed of the motor and fs > 0 is the amount of force necessary to cause the motor to stall (stop moving forward). Meanwhile, the anchor undergoes a small oscillation across the track, with position y(t) = a sin ωt relative to the track, with a and ω some positive parameters. The tether connecting the motor and the anchor is a Hookean spring with spring constant κ and rest length ℓ. The motor starts at the displacement x(t = 0) = ℓ along the track at which the tether is relaxed. An elementary two-dimensional mechanics calculation (which you might wish to pursue in your free time if you like physics, but is beside the point for this exam or class) would show this setup leads to an along-track force on the motor of: as a function of the along-track displacement x of the motor from the anchor and time t. a. (15 points) Considering the across-track oscillation of the anchor as a small disturbance, specify and conduct a nondimensionalization for the above equations which is suitable to prepare for a perturbation theory motivated by this assumption. b. (5 points) Which nondimensional parameter group would you take as a small parameter in the perturbation theory? Explain. c. (15 points) Develop a perturbation theory for the motion of the motor along the track when the across-track oscillation of the anchor can be treated as small. You should obtain the leading order behavior. explicitly, set up a fully explicit differential equation for a nontrivial correction term due to the small oscillations, and indicate how you would use the solution to this differential equation to obtain an approximation for the motion of the motor along the track. You do not need to solve the differential equation for the correction term; you just need to fully specify it so that it could be, for example, given to your coding assistant to solve numerically once your physics colleague informs your assistant of the actual values of the problem parameters. d. (5 bonus points) Express the correction term in the perturbation expansion from part c as explicitly as you can analytically. e. (10 bonus points) (Take-home only) Exhibit the nondimensional form. of your perturbation approximation numerically, choosing values of the nondimensional parameters that are consistent with the problem statement. Make sure the effect of the correction term is clearly visible. f. (5 bonus points) Over what time scale t would you expect the perturbation theory obtained by combining parts c and d to remain valid? Explain your reasoning. g. (15 bonus points) The probability the motor has remained on the track up until time t satisfies the equation: with positive parameters δ, ϕ1, and ϕ2. This evolution depends not only on the along-track force F1(x(t), t) on the motor but also the across-track force F2(x(t), t). The latter can be shown to be expressed as as a function of the along-track displacement x of the motor from the anchor and time t. Obtain an approximate expression for the probability that the motor has remained on the track up to a running time t when the across-track oscillation of the anchor can be treated as small. Your answer should involve a main term, a nontrivial correction due to the anchor disturbance, and an estimate for the error of your approximation. h. (5 bonus points) Over what (dimensional) time scale would you expect your approximation from part g to remain valid? Explain your reasoning.
Comp 330 (Fall 2024): Assignment 2 1. Let A be the automaton depicted below. (a) (10 points) Compute a minimal deterministic finite automata (DFA) from A. (b) (10 points) Using the minimal DFA to determine a regular expression representing L(A) 2. (20 points) Let Σ be a (non-empty) alphabet and let w ∈ Σ* be a string. We say that x ∈ Σ* is a prefix of the string w if there exists a string u ∈ Σ* such that w = xu. Consider the following language L = {w ∈ {a, b}* |for every prefixx of w nb (x) ≥ na (x)} Prove that L is a context-free language. Your proof should rely on mathematical induction. 3. (10 points) Compute the Chomsky Normal Form of the following context-free grammar (CFG). S → aAa|bBb|∈ A → C|a B → C|b C → CDE|∈ D → A|B|ab 4. (20 points) State whether the following claim is true or false and prove your answer. Claim: For any (non-empty) alphabet Σ, there is no language L ≤ Σ* which is both regular and inherently ambiguous. Hint: Use a context-free grammar recognizing L to show a contradiction if it were ambiguous. 5. (20 points) Build a Pushdown Automaton (PDA) recognizing the language L = {aibj |i = 2 · j}. The PDA must recognize the words by an empty stack. Briefly explain how your PDA works. Then, describe an execution of your PDA on aaaabb and show it accepts it. 6. (10 points) Use the pumping lemma to show that the language L = {an bn an bn jn ≥ 0} is not context-free.
BUSI2105-E1 A LEVEL 2 MODULE, AUTUMN SEMESTER 2022-2023 QUANTITATIVE METHODS 2A 1. Suppose that one student wanted to study the following research question: whether investing abroad can help improve a firm’s productivity? He randomly selected 12 firms, and recorded their productivities before and after they started investing abroad in the following table (assume that firm productivity follows normal distribution) : Firm 1 2 3 4 5 6 7 8 9 10 11 12 Before 1.5 1.2 1.7 1.5 2.2 2.3 2.1 1.3 1.8 1.9 2.8 2.5 After 1.8 1.6 1.9 1.8 2.7 2.3 2.6 1.4 2.3 2.2 3.2 2.6 (a) At α = 0.05, test whether productivities after firms invest abroad are higher than before. (7 Marks) (b) Does the approach adopted by this student perfectly answer his research question : does investing abroad help improve a firm’s productivity? Provide some arguments that may challenge his approach and result. (4 Marks) 2. A researcher obtains a sample with number of observations n = 100 , and population standard deviation σ = 1 . He uses this sample to formulate the following hypothesis test: H0: μ ≤ 1, and Ha : μ > 1 . He chooses the significance level α = 0.05. (a) What is the probability of making a type I error? (2 Marks) (b) What is the power of the test if the true population mean μT = 1. 1? (5 Marks) (c) How large a sample size n would be required in (b) so as to obtain a power of the test equal to 90%? (4 Marks) 3. Suppose that you want to investigate whether movie preference is associated with age. You randomly surveyed 1000 people and obtained the following contingency table. Movie Age Drama Action Comedy Others 40 140 40 70 80 At the 1% significance level, test whether movie preference is independent of age. (10 Marks) 4. Suppose that you want to compare innovation behaviour of firms across different ownership in a given industry. You randomly selected some firms in this industry, and recorded the number of patents they have applied within the same period of time. Assume that populations are normally distributed. Firm Type Private-owned State-owned Foreign-owned Number of patents 1 5 12 2 2 1 7 1 4 4 3 5 1 8 1 10 1 1 1 2 3 2 7 4 5 4 5 7 4 4 (a) At the 5% significance level, test whether the number of patents is the same between Private-owned firms and State-owned firms. (8 Marks) (b) At the 5% significance level, test whether the number of patents is the same across all types of firms. (9 Marks) 5. (a) Does the matrix have an inverse? If your answer is yes, use Gaussian elimination to find the inverse of this matrix. If your answer is no, explain why. (7 Marks) (b) Suppose f(x, y, z) = x 2 + y 2 + z 2 + xy + yz + x + z. Find the first order conditions and use Cramer’s rule to solve the stationary point(s). Determine whether each stationary point is a local minimum or maximum, or saddle. (9 Marks) 6. Bob’s utility function is given by ln x + lny − k 2 , where x and y are consumptions of two goods, and k is the number of hours spent working. (a) Optimize this utility function subject to budget constraint px + qy = wk, where p and q are prices of x and y respectively and w is the hourly wage rate. Use the Lagrangian approach to find the stationary point(s) of this optimization problem. (4 Marks) (b) Verify whether these stationary point(s) are indeed local maximum. (9 Marks) 7. Integration (a) Compute the indefinite integration (5 Marks) (b) Determine the area to the left of g(y) = 3– y2 and to the right of x = −1 . (6 Marks) 8. Difference Equations. (a) Solve 2xt + xt−1 = 6 for x0 = 1. (4 Marks) (b) Solve 6xt − 5xt−1 + xt−2 = 2 for x0 = 1 and x1 = 2 . (7 Marks)
BUSI2105-E1 A LEVEL 2 MODULE, AUTUMN SEMESTER 2021-2022 QUANTITATIVE METHODS 2A 1. Suppose that you want to test whether the performances of China’s foreign direct investment (FDI) differ across locations. You randomly select some FDI firms and record their return on equity (ROE) in the following table: Locations of FDI America Europe Asia Africa ROE 0.2 0.15 0.21 0.13 0.17 0.11 0.08 0.15 0.11 0.14 0.14 0.18 0.16 0.08 0.15 0.16 0.21 0.26 0.15 0.09 0.13 0.15 0.15 0.14 0.08 0.07 0.13 0.1 0.12 0.11 0.16 0.11 (a) What test would you use to study whether the mean ROE of these FDI differ across locations? Explain the intuition why such a test is appropriate for this research objective. (3 Marks) (b) Based on the above data, test whether the mean ROE is the same across different locations at 5% significance level. (8 Marks) 2. A researcher obtains a sample with number of observations n = 100 , and population standard deviation σ = 3. He uses this sample to formulate the following hypothesis test: H0: μ = 1, and Ha : μ ≠ 1 . He chooses the significance level α = 0.05 (a) What is the probability of making a type I error? (2 Marks) (b) What is the power of the test if the true population mean μT = 1.5? (6 Marks) (c) How large a sample size n would be required in (b) so as to obtain a power of the test equal to 90%? (4 Marks) 3. Consider the following contingency table of 600 students. Test whether subject preference is independent of gender at the 1% significance level. Subject Gender Economics Finance Accounting Management Female 100 120 50 80 Male 70 100 30 50 (10 Marks) 4. Suppose that you want to study whether the average time per day spent on homework is the same between male and female high school students. You randomly and independently collect two samples whose summary statistics are given below: Sample 1 (male) Sample 2 (female) Sample size: x y=12 ̅(y)=3.5: s y=0.8
BUSI2157 A LEVEL 2 MODULE, AUTUMN SEMESTER SPECIMEN PAPER MANAGEMENT ACCOUNTING SECTION A 1. In a process cost system, the application of manufacturing overhead usually would be recorded as a debit to: A. Finished goods. B. Manufacturing overhead. C. Cost of goods sold. D. Work in process. 2. Equivalent units for a process costing system using the weighted-average method would be equal to: A. units completed during the period and transferred out. B. units started and completed during the period plus equivalent units in the ending work in process stock. C. units completed during the period less equivalent units in the beginning stock, plus equivalent units in the ending work in process stock. D. units completed during the period plus equivalent units in the ending work in process stock. 3. Darden Company uses the weighted-average method in its process costing system. The first processing department, the Welding Department, started the month with 18,000 units in its beginning work in process stock. These units were 10% complete with respect to conversion costs. The conversion cost in this beginning work in process stock was £16,200. An additional 84,000 units were started into production during the month. 17,000 units were in the ending work in process stock of the Welding Department. These units were 70% complete with respect to conversion costs. A total of £836,880 in conversion costs were incurred in the department during the month. What would be the cost per equivalent unit for conversion costs for the month (Round off to three decimal places.) A. £8.286 B. £9.000 C. £8.804 D. £9.963 4. Which of the following is not a limitation of activity-based costing? (a) Maintaining an activity-based costing system is more costly than maintaining a traditional direct labour-based costing system. (b) Changing from a traditional direct labour-based costing system to an activity-based costing system changes product margins and other key performance indicators used by managers. Such changes are often resisted by managers. (c) In practice, most managers insist on fully allocating all costs to products, customers, and other costing objects in an activity-based costing system. This results in overstated costs. (d) More accurate product costs may result in increasing the selling prices of some products. 5. Nick Company has two products: A and B. The company uses activity-based costing. The estimated total cost and expected activity for each of the company’s three activity cost pools are as follows: Activity Cost Pool Estimated Expected Activity Cost Product A Product B Total Activity 1 £32,600 700 300 1,000 Activity 2 £17,600 600 200 800 Activity 3 £52,500 400 100 500 The activity rate under the activity-based costing system for Activity 3 is closest to: (a) £525.00. (b) £44.65. (c) £105.00. (d) £205.00. 6. A general rule in relevant cost analysis is A. variable costs are always relevant. B. fixed costs are always irrelevant. C. differential future costs and revenues are always relevant. D. depreciation is always irrelevant. 7. Opportunity costs are A. not used for decision making. B. the same as variable costs. C. the same as historical costs. D. relevant to decision making. 8. Freestone Company is considering renting Machine Y to replace Machine X. It is expected that Y will waste less direct materials than does X. If Y is rented, X will be sold on the open market. For this decision, which of the following factors is (are) relevant? I. Cost of direct materials used II. Resale value of Machine X A. Only I B. Only II C. Both I and II D. Neither I nor II 9. The variable overhead efficiency variance is most effective in measuring: A. the difference between actual variable overhead costs incurred during the period and the budget allowance based on actual input. B. the difference between actual variable overhead costs incurred during the period and the budget amount based on the time that should have been expended in producing at a certain level of activity. C. the difference between actual hours utilized in production and the standard hours allowed at a certain level of output. D. excessive usage of overhead resources. 10. Overhead is applied to work in process in a standard costing system by A. multiplying actual hours times the predetermined rate. B. multiplying standard hours allowed for the output of the period times the predetermined rate. C. multiplying actual hours times the actual rate. D. multiplying standard hours allowed for the output of the period times the actual rate. 11. A product usually sells at £20 and at this price sales are 400 units per week. During Black Friday week the price was dropped by 20% and sales increased to 600 units. The expression for the demand curve is: (a) P= 12 -0.01Q (b) P= 12 -0.02Q (c) P= 28-0.02Q (d) P= 28-0.01Q 12. Given that the demand curve for a product is P= 60- 0.05Q, marginal revenue is: (a) 60-0.1Q (b) 60-0.05Q (c) 60Q-0.05Q² (d) 60Q-0.1Q² 13. Which of the following is does not influence demand (a) Price of the good (b) Price of other goods (c) Fashion and tastes (d) The price of factors of production 14. Christmas Ltd have recently started the production of a new decoration, the Nutcracker. The first unit of the Nutcracker took 4 hours to produce and management expect a 90% learning curve to apply. What is the learning factor, to three decimal places? (a) -0.125 (b) -0.152 (c) 6.492 (d) 3.170 15. What is not a limitation of Return on Investment? (a) As a Ratio it ignores absolute size (b) It may encourage sub- optimal decisions (c) It can provide incorrect asset disposal decisions (d) It is commonly used and readily understood. 16. Which of the following is not an advantage of divisionalised organisations? (a) Quicker, more focused decisions (b) Better quality of Decisions (c) Managerial Autonomy (d) Managers pursue their own goals 17. Nutcracker Limited have a profit of £0.8m, assets of £1.6m and a cost of capital of 15%. Non-controllable fixed overheads are £0.2m, which have been deducted to arrive at the profit of £0.8m. In judging the manager’s performance, the residual income is: (a) £0.4m (b) £0.56m (c) £0.76m (d) £0.68m 18. Baubles Ltd make two products, the Angel and the Star. The standard costs relating to the Angel and the Star are: Angel Star £ £ Direct Material S 4.50 6.75 Direct Material G 3.50 1.75 Direct Labour 12.00 16.00 Variable Overhead 3.00 4.00 23.00 28.50 The Angel sells for £35 and the Star for £40. Labour and material G are found to be the binding constraints and have shadow prices of £0.81 and £1.20 respectively. The objective function for Baubles Ltd is: (a) Maximise: 11.5A + 12B (b) Maximise: 12A + 11.5B (c) Maximise: 23A + 28.5B (d) Maximise:15A +15.5B 19. Given that the extra cost of acquiring additional material is 20% of the original cost and that the Angel uses 1 Kg of material G which of the following is true (a) The Management Accountant would advise management not to buy additional Kilogrammes of G, as there would be a decrease in contribution of £4.20 (b) The Management Accountant would advise management to buy additional Kilogrammes of G, as there would be an increase in contribution of £4.20 (c) The Management Accountant would advise management not to buy additional Kilogrammes of G, as there would be a decrease in contribution of £0.50 (b) The Management Accountant would advise management to buy additional Kilogrammes of G, as there would be an increase in contribution of £0.50 20. Profit is maximised where: (a) Marginal revenue = 0 (b) Average revenue = 0 (c) Average revenue = Marginal Revenue (d) Marginal Revenue = Marginal cost SECTION B Answer one question out of two 21. Fast Foods Limited is in the food processing industry and in one of its processes, three joint products are manufactured. Traditionally, the company has apportioned work incurred up to the joint products pre-separation point on the basis of weight of output of the product. You have recently been appointed management accountant and have been investigating process costs and accounting procedures. The following process information for January 2006 is given below: Costs incurred up to separation point £192,000 Costs incurred after separation point Product X £ 40,000 Product Y £ 24,000 Product Z £ 16,000 Selling price per tonne: Completed product Estimated, if sold at separation point 1000 500 1600 1400 1200 900 Output tonnes 100 tonnes 60 tonnes 80 The cost of any unused capacity after the separation point should be ignored. You are required to prepare statements for management to show: (a) The profit or loss of each product (post separation) as ascertained using the weight basis of apportioning pre-separation point costs [15 marks] (b) The highest profit that can be achieved by the processing of these products. [15 marks] [Total 30 marks] 22. Beeston Limited, producing a range of minerals, is organised into two trading groups: one handles wholesale business and the other sales to retailers. One of its products is moulding clay. The wholesale group extracts the clay and sells it to external wholesale customers as well as to the retail group. The production capacity is 2,000 tonnes per month but at present sales are limited to 80% capacity: 1,000 tonnes wholesale and 600 tonnes retail. The transfer price was agreed at £200 per tonne in line with the external wholesale trade price. The retail group produces 100 bags of refined clay from each tonne of moulding clay which it sells at £4.00 a bag. It would sell a further 400 tonnes, if the retail trade price were reduced to £3.20 a bag. Other data relevant to the operation are: Wholesale group £ Retail group £ Variable cost per tonne 70 60 Fixed cost per month 100,000 40,000 Required a) Prepare estimated profit statement in variable costing format, showing contribution margin, for the month of December for each group and for Beeston Limited as a whole based on transfer prices of £200 per tonne when producing at: i) 80% capacity; and calculate the revised profit for each group and for Beeston Limited as a whole when producing at: ii) 100% capacity utilising the extra sales to supply the retail trade [24 marks] b) Comment on the results achieved under a) [6 marks] [Total 30 marks] SECTION C Answer one question out of two 23. Harry Draco Ltd manufactures laboratory equipment that requires a highly skilled labour force. The management have been experiencing inexplicable variances in terms of labour efficiency for quite some time and are interested when they hear that other, similar manufacturers, have implemented the learning curve which potentially provides better costing than that used currently. Management have decided to test the potential of the learning curve on a particular product, which is relatively new to the organisation. The current standard cost is specified in the table below: Material costs per unit £5,000 Standard hours per unit 140 Standard wage rate per hour £22 Standard variable overhead rate per labour hour £5 Total Fixed production cost for May £10,000 Detailed records have been kept on production of this item of equipment so the management accountant is able to extract the following information: Cumulative production units Cumulative average hours per unit Cumulative total hours 1 160 160 2 152 304 4 144.4 577.6 During month 8, May, of production the following data was recorded: Cumulative production at the beginning of May 50 units Production within May 10 units Total Material costs £49,500 Total labour cost £28,000 Total Variable cost £6,000 Total fixed cost £10,000 The management of Harry Draco Ltd would like to achieve profit maximisation but are unsure of how to achieve this and have currently set the price for this item of equipment based on a profit margin of 25%. Required: a) Calculate the expected costs for May based upon: i. the current standard cost ii. applying the learning curve formula. (13 marks) b) Calculate the price per machine based on the following, and comment upon your findings: i. the current standard cost ii. applying the learning curve formula iii. the actual cost of operations (10 marks) c) Evaluate the benefits and limitations of learning curve theory (7 marks) (Total 30 marks) Note : y = axb b = the learning index = log learning rate/log 2 24. Cycle Ltd is a company making stunt bicycles. It is a relatively new company and has so far tried to meet demand with little reference to the most profitable use of resources. As the Management accounting trainee, you have come across a new technique that you have suggested the company use, linear programming. The management of Cycle Ltd have agreed to implement this and you have therefore collected all the information that you know about the costs, resource limitations and demands for both of the bicycles in production, ‘The Kidd’ and ‘The Pastrana’. The Kidd currently makes a contribution of £1,200. It uses 12kgs of material, 10 hours of labour and 4 hours of machine time. The Pastrana makes a contribution of £1,500 uses 6kgs of material, 6 labour hours and 6 machine hours. The maximum demand for The Kidd is 400 per month. You have a limit on the resources available per month with 9,000 kgs of material, 6,000 hours of labour and 4,200 machine hours. Required: a) Formulate a linear programming problem (5 marks) b) Determine the production levels required to maximise the monthly profit using the graphical approach, clearly showing the feasible region. (12 marks) The management of Cycle Ltd have ascertained that additional machines can be hired at £200 per hour and that additional materials can be purchased at an additional cost of £4 per kg. c) Determine the shadow price of materials and machine hours and provide management with an assessment of whether it is worth purchasing additional hours of machine time and/or additional materials. Within this assessment explain the benefits and limitations of linear programming (13 marks) (Total 30 marks)
Faculty of Arts & Science Fall 2024 Quiz 9 - V1 CSC 110 Y1F Question 1. Multiple Choice Questions [3 marks] Part (a) [1 mark] def f1(numbers: list[int]) -> None: for i in range(len(numbers)): numbers[i] = i + 1 for j in range(10): print(j) Which of the following is an appropriate exact step count for the total steps the above function takes (letting n be len(numbers))? (a) n · 10 (b) n · n + 10 · 1 (c) n + 10 (d) None of these options Part (b) [1 mark] def f2(numbers: list[int]) -> int: sum = 0 for i in range(len(numbers)): for j in range(i): sum = sum + j return sum Which of the following is an appropriate, final exact step count for the total steps the above function takes in terms of input size (letting n be len(numbers))? (a) 1+ n · i +1 (b) 1+ n + i +1 (c) 1+ n · n +1 (d) None of these options Part (c) [1 mark] def f3(numbers: list[int]) -> list: new = [] for i in range(len(numbers)): new.insert(i, numbers[i]) return new Which of the following is an appropriate, final exact step count for the total steps the above function takes in terms of input size (letting n be len(numbers))? (a) 1+(n * n)+1 (b) 1+(n + n)+1 (c) 1+(n * 1) + 1 (d) 1+ 2/n(n+1) +1 (e) 1+n(2/n(n+1))+1 Question 2. Runtime analysis [5 marks] Analyse the running time of of the following function, in terms of its input length, using the same structure we did in lecture. You should clearly state how many steps each line of code takes. For each loop in the function, include the number of iterations, and number of steps per iteration. Lastly, provide the total steps as an exact step count (e.g., n2 +2n +4) and then a Theta expression (e.g., Θ(n2 )) (note: you do not need to provide any formal proof or justification for translating the exact count to its associated Theta expression, similar to what we did in lecture). def f4(n: int) -> None: i = 0 while i < n: # Loop 1 for j in range(10): # Loop 2 print(j) i = i + 4 Question 3. [4 marks] Consider the following statement: ’a, b ∈ R+, a ≥ b ∆ an ∈ Ω(bn ) a. Rewrite the above statement, but with the definition of Omega expanded. b. Prove the above statement without using any additional theorems about Omega. (Hint: your proof body should be quite short.)
Econ2Z03 Sample Exam Questions_Ch2,3,4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that the demand for artichokes (Qa) is given as: Qa = 120 - 4P At what price if any is the demand for artichokes unit elastic? A) 15 B) 10 C) 20 D) 30 2) Which of the following will NOT cause a shift in the supply of gasoline? A) An increase in the wage rate of refinery workers B) An improvement in oil refining technology C) A decrease in the price of gasoline D) A decrease in the price of crude oil 3) Plastic and steel are substitutes in the production of body panels for certain automobiles. If the price of plastic increases, with other things remaining the same, we would expect: A) the demand curve for plastic to shift to the left. B) the price of steel to fall. C) the demand curve for steel to shift to the left. D) nothing to happen to steel because it is only a substitute for plastic. E) the demand curve for steel to shift to the right. Scenario 2.1: The demand for books is: Qd = 120 - P The supply of books is: Qs = 8P+30 4) Refer to Scenario 2.1. What is the equilibrium quantity of books sold? A) 10 B) 110 C) 50 D) 75 E) none of the above 5) A vertical demand curve is A) infinitely elastic. B) highly (but not infinitely) elastic. C) completely inelastic. D) highly (but not completely) inelastic. 6) The price elasticity of gasoline supply in the U.S. is 0.4. If the price of gasoline rises by 8%, what is the expected change in the quantity of gasoline supplied in the U.S.? A) +0.32% B) -3.2% C) +3.2% D) +32.0% 7) Suppose the U.S. government imposes a maximum price of $5 per gallon of gasoline, and the current equilibrium price is $3.50 per gallon. This policy represents a: A) binding price ceiling. B) binding price floor. C) non-binding price ceiling. D) non-binding price floor. Scenario 2.2: In 1992, the Occupational Safety and Health Authority passed the Bloodborne Pathogens Standard (BBP), which regulates dental office procedures. This regulation is designed to minimize the transmission of infectious disease from patient to dental worker. The effect of this regulation was both to increase the cost of providing dental care and to ease the fear of going to the dentist as the risk of contracting an infectious disease. 8) Refer to Scenario 2.2. What is the effect of the BBP on the equilibrium price of dental care? A) It increases only if demand shifts more than supply. B) It unambiguously increases. C) It unambiguously decreases. D) It increases only if supply shifts more than demand. 9) Which of the following statements is NOT true? A) Unemployment in the economy represents an excess demand for labor. B) A surplus maybe reduced by shifting both the supply and demand curves. C) A surplus maybe reduced by shifting the demand curve rightward. D) A shortage maybe reduced by shifting the supply rightward. 10) Refer to Figure 2.1. At point D, demand is: A) elastic, but not infinitely elastic. B) inelastic, but not completely inelastic. C) unit elastic. D) unknown. E) completely inelastic. Alvin's preferences for good X and goodY are shown in the diagram below. 11) Based on Figure 3.2, it can be inferred that: A) Alvin regards good X and goodY as perfect complements. B) Alvin does not consider good X as "good." C) Alvin regards good X and goodY as perfect substitutes. D) Alvin will never purchase any of goodY. E) none of the above 12) An upward sloping indifference curve defined over two goods violates which of the following assumptions from the theory of consumer behavior? A) more is preferred to less. B) transitivity. C) preferences are complete. D) all of the above E) none of the above 13) Mikey is very picky and insists that his mom make his breakfast with equal parts of cereal (C) and apple juice (A). Any other combination and it ends up on the floor. Mikey's utility function of consuming cereal and apple juice is U=min(C, A). Cereal costs 4 cents per tablespoon and apple juice costs 6 cents per tablespoon. If Mikey's mom budgets $8 per month for Mikey's breakfast, how much cereal and juice does she buy? A) 100 tablespoons of cereal and 67 tablespoons of juice B) 40 tablespoons of cereal and 75 tablespoons of juice C) 80 tablespoons each of cereal and juice D) 40 tablespoons each of cereal and juice 14) The endpoints (horizontal and vertical intercepts) of the budget line: A) indicate the highest level of satisfaction the consumer can achieve. B) measure the rate at which one good can be substituted for another. C) represent the quantity of each good that could be purchased if all of the budget were allocated to that good. D) measure the rate at which a consumer is willing to trade one good for another. E) measure its slope. 15) If the quantity of good A (QA) is plotted along the horizontal axis, the quantity of good B (QB) is plotted along the vertical axis, the price of good A is PA, the price of good B is P B and the consumer's income is I, then the slope of the consumer's budget constraint is . A) -PA/P B B) I/PA or I/P B C) -QB/Q A D) -PB/PA E) -QA/QB 16) The fact that Alice spends no money on travel: A) implies that her MRS does not equal the price ratio. B) implies that she is at a corner solution. C) implies that she does not derive any satisfaction from travel. D) any of the above are possible. 17) Bill currently uses his entire budget to purchase 5 cans of Pepsi and 3 hamburgers per week. The price of Pepsi is $1 per can, the price of a hamburger is $2, Bill's marginal utility from Pepsi is 4, and his marginal utility from hamburgers is 6. Bill could increase his utility by: A) increasing Pepsi consumption and reducing hamburger consumption. B) maintaining his current consumption choices. C) increasing hamburger consumption and reducing Pepsi consumption. D) We do not have enough information to answer this question. 18) The magnitude of the slope of an indifference curve is: A) always equal to the ratio of the prices of the goods. B) called the marginal rate of substitution. C) equal to the ratio of the total utility of the goods. D) all of the above E) A and C only 19) The curve in the diagram below is called A) the price-consumption curve. B) the income-consumption curve. C) the demand curve. D) the Engel curve. E) none of the above 20) The change in the price of one good has no effect on the quantity demanded of another good. These goods are: A) complements. B) both Giffen goods. C) both inferior. D) substitutes. E) none of the above 21) As we move downward along a demand curve for apples, A) the marginal utility of apples decreases. B) consumer well-being decreases. C) the marginal utility of apples increases. D) Both A and B are true. E) Both A and C are true. 22) The income-consumption curve for Dana between Qa and Qb is given as: Qa = Qb. His budget constraint is given as: 120 = Qa + 4Qb How much Qa will Dana consume to maximize utility? A) 0 B) 30 C) 60 D) 24 E) More information is needed to answer this question. 23) Your income response for bicycle riding changes with the amount of income you earn. At low levels of income, you view bicycle riding as an inferior good and substitute other types of transportation (e.g., auto travel) as your income rises. However, you view bicycle riding as a normal good after your income rises above a particular level. What shape does your Engel curve for bicycle riding have? A) C-shaped B) Horizontal line C) Vertical line D) Upward sloping E) none of the above Scenario 4.1: Daniel derives utility from only two goods, cake (Qc) and donuts (Qd). The marginal utility that Daniel receives from cake (MUc) and donuts (MUd) are given as follows: MUc = Qd MUd = Qc Daniel has an income of $240 and the price of cake (Pc) and donuts (Pd) are both $3. 24) See Scenario 4.1. What quantity Qc will maximize Daniel's utility given the information above? A) 60 B) 0 C) 40 D) 24 E) none of the above 25) Use the following statements to answer this question: I. A price-consumption curve is derived by varying the price of asparagus. If the price-consumption curve is an upward sloping straight line, the demand curve for asparagus must be downward sloping. II. Fred consumes only food and clothing. Fred's Engel curve traces out the utility maximizing combinations of food and clothing associated with each and every income level. A) I and II are false. B) I is true, and II is false. C) I is false, and II is true. D) I and II are true. Use the figure below to answer the following questions. 26) Which one of the graphs in Figure 9.2.1 shows perfect substitutes? A) (a) B) (b) C) (c) D) (d) E) (c) and (d) 27) The shape of a person's indifference curves between two goods depends on A) the degree of substitutability between the two goods. B) the prices of the two goods. C) the level of satisfaction for the person. D) the person's income. E) all of the above. 28) Suppose the price of potatoes falls and there is a decrease in the purchases of potatoes, what can we infer? A) The income effect is negative and exceeds the substitution effect. B) The income effect is negative and reinforces the substitution effect. C) The income effect is positive and reinforces the substitution effect. D) The income effect is negative and just about offsets the substitution effect. E) The income effect is positive and exceeds the substitution effect. Use the figure below to answer the following questions. 29) Consider an initial budget line labelled RS in Figure 9.3.3. If the budget line becomes RT, the income effect is illustrated by the move from point A) A to B. B) A to C. C) A to D. D) B to C. E) B to D. 30) The following data pertain to products A and B, both of which are purchased by Madame X. Initially, the prices of the products and quantities consumed are: PA= $10, QA= 3, PB = $10, QB = 7. Madame X has $100 to spend per time period. After a reduction in price of B, the prices and quantities consumed are: PA= $10, QA= 2.5, PB= $5, QB = 15. Assume that Madame X maximizes utility under both price conditions above. Also, note that if after the price reduction enough income were taken away from Madame X to put her back on the original indifference curve, she would consume this combination of A and B: QA = 1.5, QB = 9 Determine the substitution effect. A) 2 B) 4 C) 6 D) 8
Faculty of Arts & Science Fall 2024 Quiz 9 - V2 CSC 110 Y1F Question 1. Multiple Choice Questions [4 marks] Part (a) [1 mark] def f1(numbers: list[int]) -> None: for i in range(len(numbers)): numbers[i] = i ** 2 for j in range(len(numbers)): print(j) Which of the following is an appropriate exact step count for the total steps the above function takes (letting n be len(numbers))? (a) n · n (b) n + n (c) n + n2 (d) n + 2n(n+1) Part (b) [2 marks] def f2(numbers: list[int]) -> None: for i in range(10): numbers.append(i) for j in range(len(numbers)): print(j) Which of the following is an appropriate exact step count for the total steps the above function takes (letting n be len(numbers) when f2 is called)? (a) n * 10 + 10 * 1 (b) n * n + 10 * 1 (c) n * 10 (d) None of these options Part (c) [1 mark] def f3(numbers: list[int]) -> None: squares = [x ** 2 for x in numbers] for i in range(len(squares)): print(i) Which of the following is an appropriate, final exact step count for the total steps the above function takes in terms of input size (letting n be len(numbers) when f3 is called)? (a) n · n (b) n + n (c) n + n2 (d) n + 2n(n+1) Question 2. Runtime analysis [5 marks] Analyse the running time of the following function, in terms of its input length, using the same structure we did in lecture. You should clearly state how many steps each line of code takes. For each loop in the function, include the number of iterations, and number of steps per iteration. Lastly, provide the total steps as an exact step count (e.g., n2 +2n +4) and then a Theta expression (e.g., Θ(n2 )) (note: you do not need to provide any formal proof or justification for translating the exact count to its associated Theta expression, similar to what we did in lecture). def f4(n: int) -> int: i = 1 sum = 0 while i < n: sum = sum + i i = i * 2 return sum Question 3. [4 marks] Consider the following statement: ’a, b ∈ R+ , a ≤ b ∆ na + nb ∈ O(nb) a. Rewrite the above statement, but with the definition of Big O expanded. b. Prove the above statement without using any additional theorems about Big O.
MTH205 Introduction to Statistical Methods Tutorial 7 Based on Chapter 7 1. You are given the following data x y 0.0 10.9 0.0 10.6 0.0 10.8 0.0 9.8 0.0 9.0 2.3 11.0 2.3 11.3 2.3 9.9 2.3 9.2 2.3 10.1 4.6 10.6 4.6 10.4 4.6 8.8 4.6 11.1 4.6 8.4 9.2 9.7 9.2 7.8 9.2 9.0 9.2 8.2 9.2 2.3 18.4 2.9 18.4 2.2 18.4 3.4 18.4 5.4 18.4 8.2 with Sxx = 1058, Syy = 198.76 and Sxy = −363.63. Using the simple linear regression model Yi = β0 + β1xi + ; i = 1, 2,..., 25 where the are independent and normally distributed with zero means and equal variances σ2, obtain the least squares estimates of β0 and β1. Carry out a lack-of-fit test to determine the adequacy of the simple linear regression model at the 5% level of significance. Interpret the results.
LC – Anthropology of Africa Module Code: 09 28904 Assessment weighting: 70% You should write an essay of 2000 words in response to the essay question listed below. For further guidance on the format and submission of the essay see the module canvas page. Assignment Deadline: 15 January 2025 by 12 noon (UK time) Question: To what extent does the colonial encounter continue to shape anthropological knowledge of Africa today? Instructions: For 2000 words, I recommend that you draw on three or four full ethnographic case studies, although you might also reference other anthropological literature studied in this module. You can either focus on one weekly topic/theme of the module, or you can draw on case studies and engage with debates from across the module. NB: Essays submitted later than the deadline will incur a penalty of 5 marks per working day (12 noon is the end of a working day for these purposes). Penalties will also be applied if you go more than 100 words above the word limit of 2000 words. This word limit includes quotations, references, and footnotes, but not your bibliography.
BUSI2157-E1 A LEVEL 2 MODULE, AUTUMN SEMESTER 2021-2022 MANAGEMENT ACCOUNTING Section B (40 marks) Answer ONE question Question 1 Company G has a machining facility specializing in work for the aircraft components market. The prior job-costing system had two direct-cost categories (direct materials and direct manufacturing labour) and a single indirect-cost pool (manufacturing overhead, allocated using direct labour-hours). The indirect cost-allocation rate of the prior system for the year would have been £115 per direct manufacturing labour-hour. Recently, a team with members from product design, manufacturing and accounting used an activity-based approach to refine its job-costing system. The two direct-cost categories were retained. The team decided to replace the single indirect-cost pool with five indirect-cost pools. These five cost pools represent five activity areas at the facility, each with its own supervisor and budget responsibility. Pertinent data are as follows: Activity area Cost driver used as allocation base Cost-allocation rate £ Materials handling Parts 0.40 Lathe work Turns 0.20 Milling Machine-hours 20.00 Grinding Parts 0.80 Testing Units tested (all units have to be tested) 15.00 Information-gathering technology has advanced to the point where all the data necessary for budgeting in these five activity areas are automatically collected. Two representative jobs processed under the new system at the facility in the most recent period had the following characteristics: Job A Job B Direct materials cost per job £9,700 £59,900 Direct manufacturing labour cost per job £750 £11,250 Direct manufacturing labour-hours per job 25 375 Parts per job 500 2,000 Turns per job 20,000 60,000 Machine-hours per job 150 1,050 Units per job 10 200 Required: (a) Calculate the per unit manufacturing costs of each job under the prior job- costing system. (6 marks) (b) Calculate the per unit manufacturing costs of each job under the activity-based-costing system. (14 marks) (c) Compare the per unit cost figures for Jobs A and B calculated in requirements (a) and (b). Explain why the prior and the activity-based costing systems differ in their job cost estimates for each job? Why might these differences be important to Company G? (14 marks) (d) Assume the company uses ‘total cost plus’ pricing. Explain TWO disadvantages of ‘total cost plus’ pricing. (6 marks) (Total 40 marks) Question 2 Cars Ltd, a local garage, which has a body shop. The body shop manager has contacted a management accountant, saying that one of the company’s present customers has offered the company a one-year contract for additional work. The customer requires a discount of 10 per cent to be allowed on the total invoice value. The manager provides the accountant with the following information: 1. Additional capital expenditure will be: £ Video conferencing facility 10,000 Additional storage trolleys 5,000 Computerised estimated system 10,000 The customer insists on installation of the video conferencing facility which will not be usable for any other contract. The storage trolleys and estimating system may be used on other work after the end of this particular contract. 2. Additional staff will be required. Three full-time skilled technicians earning £8.00 per hour will each work 39 hours per week on the new contract. They are each allowed 6 weeks per year paid holidays and 2 weeks paid training. Labour efficiency is 95 per cent measured as the ratio of sold hours/hours occupied. Training time and holiday time are charged to direct costs of the department. For each technician the new contract will leave some unsold hours available for any other jobs coming into the body shop. One full-time car cleaner will be required earning £10,500 per annum. 3. The customer has said that the potential increase in sales due to chargeable hours from this contract could be 4,500 hours at a rate of £20.00 per hour before discount. In addition, the increase in sales of car parts is calculated on the basis of £40.00 per hour with an average gross profit of 15 per cent before discount. The increase in paint sales is calculated on the basis of £3.50 per hour with an average gross profit of 40 per cent before discount. 4. Additional annual overheads will be as follows: £ Variable costs 5,500 Fixed costs 6,500 5. Depreciation is calculated on a straight-line basis as follows: % Storage trolleys 20 Computers 25 The manager has asked for an opinion on the acceptability of the customer’s proposal. Required: Write a memo to the manager: (a) Assessing the financial aspects of the proposal under the relevant costing principles and based on that to give suggestion. (30 marks) (b) Commenting on other considerations relevant to the decision-making process. (10 marks) (Total 40 marks) Section C (40 marks) Answer ONE question Question 1 Nottingham Products, Inc., has a Calculator Division that manufactures and sells a standard calculator: Capacity in units 100,000 Selling price to outside customers £30 Variable costs per unit £16 Fixed costs per unit (based on capacity) £9 The company has a Notebook Division that could use this calculator in one of its notebooks. The Notebook Division is currently purchasing 10,000 calculators per year from an overseas supplier at a cost of £29 per calculator. Required: (a) Assume that the Calculator Division has enough idle capacity to handle all of the Notebook Division’s needs. What is the acceptable range, if any, for the transfer price between the two divisions? (8 marks) (b) Assume that the Calculator Division is selling all of the calculators that it can produce to outside customers. What is the acceptable range, if any, for the transfer price between the two divisions? (8 marks) (c) Assume again that the Calculator Division is selling all of the calculators that it can produce to outside customers. Also assume that £3 in variable expenses can be avoided. What is the acceptable range, if any, for the transfer price between the two divisions? (8 marks) (d) Refer to the original data in the question setting. Assume that the Notebook Division needs 20,000 special calculators per year. The Calculator Division’s variable costs to manufacture and ship the special calculator would be £20 per unit. To produce these special calculators, the Calculator Division would have to reduce its production and sales of regular calculators from 100,000 units per year to 70,000 units per year. As far as the Calculator Division is concerned, what is the lowest acceptable transfer price? (8 marks) The following table sets out information in respect of Calculator Division and Notebook Division. Division X Division Y Amount to be invested in new project £4m £4m Sales from the new project £2m £2m Net profit from the new project £1.2m £0.8m ROI of existing investment 33% 4% The cost of borrowing new finance is 10% per annum. (e) Explain what view the managers of each division might take, depending on the method of performance evaluation applied. (8 marks) （Total 40 marks） Question 2 RST manufactures three products using different quantities of the same resources. Details of these products are as follows: Product R S T £/unit £/unit £/unit Market selling price 90 126 150 Direct labour (£7/hour) 14 28 35 Material A (£3/kg) 15 12 21 Material B (£6/kg) 24 36 30 Variable overhead (£4/hour) 8 16 20 Fixed overhead 12 7 12 73 99 118 Profit 17 27 32 The management of RST has predicted the demand for these products for July as follows: Product R 500 units Product S 800 units Product T 1,600 units These demand estimates do NOT include an order from a major customer to supply 400 units per month of each of the three products, at a discount of £10 per unit from the market selling price. During July, the management of RST anticipate that there will be a shortage of material B, and that only 17,500 kgs will be available. It is not possible for RST to hold inventory of any raw materials, work in progress or finished products. Required: (a) Prepare calculations to show the optimum product mix to maximise RST’s profit for July, assuming that the order with the major customer is supplied in full. (10 marks) RST has now realised that the contract with the major customer does not have to be met in full for any of the three products. The customer will accept whatever RST is prepared to supply at the contracted prices but they will change a financial penalty if RST does not supply them in full in July. (b) Calculate the lowest value of the financial penalty that the major customer would need to insert in the contract to ensure that RST meets its order in full in July. (10 marks) Now that you have presented your answer to (a) and (b) above to the management team of RST, the production manager has advised that, due to holidays, the number of direct labour hours available will be reduced to a total of 9,800 hours in July. A decision has been made that RST will fulfil its order with the major customer in full in July and it has been agreed that a linear programming model will be used to determine optimum usage of the resources that will be available after setting aside those required for the major customer’s order. (c) Identify the objective function and the constraints to be used in the linear programming model to determine the optimum usage of the remaining resources to maximise the company’s profits for July. (6 marks) (d) The optimal solution has been determined as: R 500 units S 0 units T 880 units Explain which of the constraints you stated in (c) are binding on the solution. (You are not required to draw a graph.) (4 marks) (e) Critically evaluate the benefits and limitations of using linear programming for planning purposes. (10 marks) (Total 40 marks)
Business Analytics: review problems. Solutions provided at the end. Problem 1: A company produces two products, A and B. Each unit of A requires 1, 3 and 2 kilograms of wood, plastic and steel respectively and each unit of B requires 3, 4 and 1 kilograms of wood, plastic and steel respectively. A maximum of 240, 360, and 180 kilograms of wood, plastic and steel available. The profit per unit of A and B is $4.00 and $6.00 respectively. The objective is to maximize total profits. Formulate this as a linear programming model. Problem 2: A manufacturer produces desks and chairs. Each desk uses 5 units of wood and each chair uses 3 units of wood. Total wood available for a month is 2200 units. Desk production requires 3 hours of labor and a chair needs 1.4 hours. Total number of hours available per month: 1150. Each desk contributes 40 dollars to profit and each chair contributes $22. Marketing requires that at least 3 chairs be produced for each desk produced. The objective is to maximize total profits. Note: you can ignore the integer requirements. Formulate this as a linear programming model Problem 3: A resort hotel is being built in a wooded area. Four locations (“nodes”) are to be connected with paths. All locations must be connected. Building paths is costly, so the objective is to minimize the total distance of building all the paths. Formulate this as a linear program. Table 1 Node Node Distance 1 2 110 1 3 150 1 4 190 2 3 215 2 4 275 3 4 310 1 Hotel 2 Tennis courts 3 Pool 4 Spa Problem 4: Formulate an integer linear programming problem from the information provided below: We want to buy two types of machines (M1 and M2); use variables X1 and X2 to denote number of machines of two types. Objective function: Marginal daily profitability per unit of M1 and M2 is 100 dollars and 150 dollars and you want to maximize your total daily profitability. Resource and production constraints: · M1 costs 15000 dollars per unit and M2 costs 4000 dollars. Your budget: 140,000 dollars. · Space available: 200 square feet. M1 needs 15 square feet per unit and M2 needs 25 square feet per unit. · Number of machines of type M1 must be at least twice as many as type M2. List integer and/or other constraints at the end. Problem 5: Table 1 shows the payoff values for 3 alternative investment options and 3 events. Which alternative would you select if you use Mini-max regret approach? Table 1: Payoff table Table 2: Regret table Rates up Rates static Rates down Rates up Rates static Rates down Stocks -4 4 12 Stocks Bonds -2 3 8 Bonds Money M 3 2 1 Money M. Problem 6: Table 1: Payoff Events E1 E2 E3 A1 250 80 30 A2 150 140 130 Prob. 0.6 0.1 0.3 Table 1 below shows the payoff values with two alternatives A1 and A2. Each alternative has three chance events (E1, E2 and E3) with probabilities shown. Draw a tree diagram, calculate expected value (EV) for each alternative and select the preferred alternative under risk-neutrality. Problem 7: A company has to decide whether to expand or not. The expansion cost is $2.1 million. If the economy improves substantially (20% probability) the (projected) revenues with expansion will be $6.0 million. If the economy turns worse (30% probability) the revenues will be $2.1 million. With economy remaining roughly the same (50% probability), the revenues will be 4.2 million. Without expansion, the corresponding revenues will be $3.0 million, $1.2 million and 1.9 million. (a) Draw a decision tree and calculate the expected value of each alternative. (b) What decision would you recommend to a risk-neutral decision-maker? Do not forget to take into account the cost of expansion. Problem 8 (from 2018 final exam): The associate dean at the Karey Business School needs to allocate instructors to the courses offered in the next semester. There are three instructors, each of whom will be teaching exactly one module. The past evaluation scores of these instructors are as follows: Prof. Ford 60 Prof. Johnson 80 Prof. Hoover 50 There are 3 modules, each of which has a different number of students, as shown below: Module 1: Leadership (qualitative) 35 students Module 2: Data analysis (quantitative) 45 students Module 3: Financial modeling (quantitative) 50 students (a) (5 points) The associate dean wants to build a model for assigning the instructors to the modules. Define the decision variables for this model. (b) (10 points) Formulate a linear program with the objective to maximize total satisfaction (the sum of satisfaction of all students). You can assume that past evaluation scores reflect the satisfaction with each instructor, and that each instructor is capable of teaching each module. Qualitative courses Quantitative courses Prof. Ford 55 75 Prof. Johnson 80 80 Prof. Hoover 70 60 (c) (10 points) It has been noticed that the instructors received different evaluation scores in the different courses they have taught. The scores are as follows: Specifically, the dean wants to use the evaluation scores for qualitative courses to predict student satisfaction in module 1, and the evaluation scores for quantitative courses to predict student satisfaction in modules 2 and 3. Formulate a new model using these separate evaluation scores. Problem 9 (from 2019 final exam) You have built a fast food business and are now considering selling it. There are several potential acquirers, and you plan to determine the sale price in a sealed bid auction. Under the rules of the auction, the price would be the highest bid. Due to their limited information the acquirers may underestimate or overestimate what the business is worth. You have received indication that McDonald’s valuation of your business is uniformly distributed between $100 Million and $120 Million, and that Burger King’s valuation of your business is uniformly distributed between $100 Million and $150 Million. You believe that both companies will bid their valuation during the auction. In preparation for the auction you want to use simulation to see how much money you can make. You have generated the following random numbers from the [0,1] uniform. distribution (each of the ten numbers has been generated independently): McDonald’s Burger King Trial 1 0.46 0.06 Trial 2 0.56 0.68 Trial 3 0.97 0.33 Trial 4 0.74 0.73 Trial 5 0.15 0.12 (a) (2 points) How can you use these numbers to predict the bids and the final sale price? Describe the approach. (b) (4 points) Given the numbers in the table above, what sale price do you expect, on average? (c) (2 points) The bidders have an instinct about the Winner’s curse and they each plan to bid only 75% of their valuation (Winner’s curse is a phenomenon where the winner generally overpays during competitive bidding). How would that change your answer to (b)? (d) (2 points) BARM Analytica, a startup out of Washington DC, offers to identify an additional bidder whose valuation is equally likely to be 100, 120 or 140. How large a fee should you be willing to pay for this service assuming that each bidder bids their true valuation? Use simulation and the following uniform. [0,1] random numbers: 0.11, 0.65, 0.89, 0.23, 0.53 to justify your answer.
Econ2Z03 Sample Exam Questions_Ch5,6,7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) What describes the graphical relationship between average product and marginal product? A) Average product cuts marginal product from below, at the maximum point of marginal product. B) Marginal product cuts average product from below, at the maximum point of average product. C) Average and marginal product do not intersect. D) Average product cuts marginal product from above, at the maximum point of marginal product. E) Marginal product cuts average product from above, at the maximum point of average product. 2) Consider the following statements when answering this question; I. Suppose a semiconductor chip factory uses a technology where the average product of labor is constant for all employment levels. This technology obeys the law of diminishing returns. II. Suppose a semiconductor chip factory uses a technology where the marginal product of labor rises, then is constant and finally falls as employment increases. This technology obeys the law of diminishing returns. A) Both I and II are true. B) I is true, and II is false. C) Both I and II are false. D) I is false, and II is true. 3) A manufacturing firm uses only capital (K) and labour (L) to produce its product, using a production function of Q = 10KL. It pays its workers w = $15 per hour and has a rental cost of capital of r = $5 per hour. If the firm wants to produce 480 units of output, the optimal bundle of inputs is: A) (4, 12). B) (3, 16). C) (12, 4) D) (6, 8). 4) The law of diminishing returns assumes that A) there is at least one fixed input. B) all inputs are held constant. C) additional inputs are added in smaller and smaller increments. D) all inputs are changed by the same percentage. 5) Use the following two statements to answer this question: I. The marginal product of labor is the slope of the line from the origin to the total product curve at that level of labor usage. II The average product of labor is the slope of the line that is tangent to the total product curve at that level of labor usage. A) I is true, and II is false. B) I is false, and II is true. C) Both I and II are true. D) Both Iand II are false. Figure 6.1 6) Refer to Figure 6.1. Which of the following statements is false? A) At point E the marginal product of labor is less than the average product of labor. B) At point E the average product of labor is negative. C) At point E the marginal product of labor is negative. D) At point E the average product of labor is decreasing. E) At point E the marginal product of labor is decreasing. 7) If capital is measured on the vertical axis and labor is measured on the horizontal axis, the slope of an isoquant can be interpreted as the A) marginal product of capital. B) average rate at which the firm can replace capital with labor without changing the output rate. C) marginal product of labor. D) rate at which the firm can replace capital with labor without changing the output rate. 8) An examination of the production isoquants in the diagram below reveals that: A) capital and labor must be used in fixed proportions. B) capital and labor are perfectly substitutable. C) the MRTS is constant along the isoquant. D) Both B and C are correct. E) none of the above 9) The diagram below shows an isoquant for the production of wheat. Which point has the highest marginal productivity of labor? A) Point A B) Point B C) Point C D) Point D 10) Which of the following examples represents a fixed-proportion production system with capital and labor inputs? A) Airplanes and pilots B) Horse-drawn carriages and carriage drivers C) Clerical staff and computers D) all of the above Figure 6.2 11) Refer to Figure 6.2. The situation pictured is one of A) increasing returns to scale, because doubling inputs results in more than double the amount of output. B) constant returns to scale, because the line through the origin is linear. C) increasing returns to scale, because the isoquants are convex. D) decreasing returns to scale, because the isoquants are convex. E) decreasing returns to scale, because doubling inputs results in less than double the amount of output. 12) A farmer uses M units of machinery and L hours of labor to produce C tons of corn, with the following production function C = L0.5M0.75. This production function exhibits A) constant returns to scale for all output levels B) increasing returns to scale for all output levels C) no clear pattern of returns to scale D) decreasing returns to scale for all output levels 13) A farmer uses M units of machinery and L hours of labor to produce C tons of corn, with the following production function Q = L0.5 + M0.75. This production function exhibits A) decreasing returns to scale for all output levels. B) constant returns to scale for all output levels. C) increasing returns to scale for all output levels. D) no clear pattern of returns to scale. 14) In 1985,Alice paid $20,000 for an option to purchase ten acres of land. By paying the $20,000, she bought the right to buy the land for $100,000 in 1992. When she acquired the option in 1985, the land was worth $120,000. In 1992, it is worth $110,000. Should Alice exercise the option and pay $100,000 for the land? A) It depends on what the rate of inflation was between 1985 and 1992. B) Yes. C) No. D) It depends on what the rate of interest was. 15) The difference between the economic and accounting costs of a firm are A) the corporate taxes on profits . B) the sunk costs incurred by the firm. C) the accountant's fees. D) the explicit costs of the firm. E) the opportunity costs of the factors of production that the firm owns. 16) Jim left his previous job as a sales manager and started his own sales consulting business. He previously earned $70,000 per year, but he now pays himself $25,000 per year while he is building the new business. What is the economic cost of the time he contributes to the new business? A) $25,000 per year B) zero C) $45,000 per year D) $70,000 per year 17) In a short-run production process, the marginal cost is rising and the average variable cost is falling as output is increased. Thus, A) marginal cost is below average fixed cost. B) average fixed cost is constant. C) marginal cost is above average variable cost. D) marginal cost is below average variable cost. 18) A firm employs 100 workers at a wage rate of $10 per hour, and 50 units of capital at a rate of $21 per hour. The marginal product of labor is 3, and the marginal product of capital is 5. The firm A) could reduce the cost of producing its current output level by employing more capital and less labor. B) is producing its current output level at the minimum cost. C) could reduce the cost of producing its current output level by employing more labor and less capital. D) could increase its output at no extra cost by employing more capital and less labor. E) Both B and D are true. 19) If two different fuel sources (e.g., coal and natural gas) are perfect substitutes in the long-run production of energy. How will a profit maximizing firm choose between these two inputs? A) The firm will only use the input with higher cost B) The firm cannot achieve a profit maximizing level of output under these circumstances C) The firm will use equal amounts of the two inputs, even if one of the inputs has a lower cost D) The firm will only use the input with lower cost 20) At the current level of output, long-run marginal cost is $50 and long-run average cost is $75. This implies that: A) there are neither economies nor diseconomies of scale. B) there are diseconomies of scale. C) the cost-output elasticity is greater than one. D) there are economies of scale. 21) The equation below gives the degree of economies of scope (SC): SC = (C(Q1) + C(Q2) - C(Q1,Q2)) / C(Q1,Q2) where C(Q1) is the cost of producing output Q1, C(Q2) is the cost of producing output Q2, and C(Q1,Q2) is the joint cost of producing both outputs. If SC is negative: A) there are neither economies nor diseconomies of scope. B) there are economies of scope. C) there are diseconomies of scope. D) there are both economies and diseconomies of scope. Figure 5.1.1 22) Refer to Figure 5.1.1 above. Which of the two jobs is more risky? A) Job 1 B) Job 2 C) Both are equally risky. D) Neither job is risky. The information in the table below describes choices for a new doctor. The outcomes represent different macroeconomic environments, which the individual cannot predict. Table 5.3 Outcome 1 Outcome 2 Job Choice Prob. Income Prob. Income Work for HMO 0.95 $100,000 0.05 $60,000 Own practice 0.2 $250,000 0.8 $30,000 Research 0.1 $500,000 0.9 $50,000 23) Refer to Table 5.3. The expected returns are highest for the physician who: A) opens her own practice. B) does research. C) either opens her own practice or does research. D) either works for an HMO or does research. E) works for an HMO. 24) The expected value is a measure of: A) uncertainty. B) central tendency. C) variability. D) risk. 25) Blanca would prefer a certain income of $20,000 to a gamble with a 0.5 probability of $10,000 and a 0.5 probability of $30,000. Based on this information: A) we can infer that Blanca neutral. B) we can infer that Blanca is risk loving. C) we can infer that Blanca is risk averse. D) we cannot infer Blanca's risk preferences. Figure 5.2.2 26) When facing a 50% chance of receiving $50 and a 50% chance of receiving $100, the individual pictured in Figure 5.2.2: A) would want to be paid a risk premium of 10 utils to give up the opportunity of facing the two outcomes. B) would pay a risk premium of 10 utils to avoid facing the two outcomes. C) would want to be paid a risk premium of $7.50 to avoid facing the two outcomes. D) would pay a risk premium of $7.50 to avoid facing the two outcomes. E) has a risk premium of 10 utils. Scenario 5.8: Risk-neutral Icarus Airlines must commit now to leasing 1, 2, or 3 new airplanes. It knows with certainty that on the basis of business travel alone, it will need at least 1 airplane. The marketing division says that there is a 50% chance that tourism will be big enough for a second plane only. Otherwise, tourism will be big enough for a third plane. This, plus revenue information, yields the following table: Planes Tourism Revenue Expected Leased 2 3 Light Heavy $90 million $30 million $10 million $140 million Profit $60 million $75 million 27) Refer to Scenario 5.8. Given that the two outcomes are equally likely, Icarus Airlines' expected profit under complete information would be: A) $120 million. B) $40 million. C) $90 million. D) $125 million. E) $115 million. 28) We may not be able to fully remove risk by diversification if: A) buying stock on margin is not allowed by financial regulators. B) a completely risk-free asset does not exist. C) the asset returns in our portfolio are positively correlated. D) none of the above 29) Suppose our firm produces chartered business flights with capital (planes) and labor (pilots) in fixed proportion (i.e., one pilot for each plane). The expansion path for this business will: A) not be defined. B) be a vertical line. C) follow the 45-degree line from the origin. D) increase at a decreasing rate because we will substitute capital for labor as the business grow. 30) Davy Metal Company produces brass fittings. Q = 500L0.6K0.8, where Q = annual output measured in pounds, L = labor measured in person hours, K = capital measured in machine hours. The marginal products of labor and capital are: MPL = 300L-0.4K0.8 MP K = 400L0.6K-0.2 Davy's employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Determine the firm's optimal capital-labor ratio, given the information above. A) 2.5 B) 0.3 C) 3.3 D) 0.4
BUSI2105-E1 A LEVEL 2 MODULE, AUTUMN SEMESTER 2020-2021 QUANTITATIVE METHODS 2A 1. To stimulate the economy after COVID-19 pandemic, many cities in China introduced the consumer coupon. A researcher wants to study whether such consumer coupon has effectively increased the number of households’ transactions within a given period of time, so he collects a sample of cities that have introduced the consumer coupon and a sample of cities that have not. The summary statistics are listed below (assume that the two populations are normally distributed) : (a) At α = 0.01, test whether the consumer coupon has effectively increased the number of transactions (assume equal population variance). (10 Marks) (b) In your opinion, what are the potential problems of the above test of difference in means using independent samples? Explain why it could be better to use matched samples in this case. (6 Marks) 2. Suppose that you want to study the performances in QM2A of students from different majors. You randomly select some students and record their marks of final exam in the following table, categorizing these students according to the majors they belong to. Majors to which students belong FAM IBE Others Marks Of QM2A 80 72 66 73 85 90 88 72 67 79 71 67 70 85 89 84 73 66 78 75 69 70 77 80 76 75 75 (a) If you want to investigate whether the mean mark of students is the same across the above three majors, what test would you use? Explain the intuition of how such test can achieve this research objective. (4 Marks) (b) Based on the above data, test whether the mean mark is the same across different majors at the 5% significance level. (12 Marks) (c) At the 10% significance level, test whether the variance of marks is the same between FAM students and IBE students. (8 Marks) 3. Consider the following linear simultaneous equation system in x, y, z. x − y + z = 1 (1) 2x + y + z = 4 (2) 5y + 2z = 7 (3) (a) Express this system in matrix form. AX = b, with vector X = [x y z]T . Find the inverse of the coefficient matrix A using its determinant and adjoint matrix. (10 Marks) (b) Solve the system using Cramer’s Rule. (6 Marks) 4. A household has the utility function U = ln(q1) + ln(q2), where q1 and q2 are the quantities of consumption of two types of goods. The budget constraint is given by p1 q1 + p2 q2 = 200, where p1 and p2 are prices of q1 and q2 respectively. The household is a price taker. (a) Using the Lagrange function approach, determine the optimal quantities of consumption q1 and q2 that maximize the household’s utility (taking the prices as given). (6 Marks) (b) Based on the Bordered Hessian verify that your solution indeed constitutes a maximum of utility. (6 Marks) (c) If the price for goods 1 increases from p1 = 5 to p1(′) = 10, other things equal, how large is the loss of the household’s consumer surplus? (6 Marks) 5. The inventory of a firm Qt adjusts as follows: Qt+1 = PQ t + τIt where It is the investment that adds new inventory. P captures the depreciation of inventory such that each period, 1 − P share of the inventory is lost, and 0 < P < 1 . τ measures the efficiency of transforming investment into inventory, and 0 < τ < 1 . (a) If investment It is a constant It = I(̅), express Qt as a function of t (assume that the initial inventory is Q0 ) (3 Marks) (b) If It = I(̅) + βQt , where β captures the reaction of investment to the current inventory level, express Qt as a function of t (assume that Q0 is known). (5 Marks) (c) Discuss the dynamic trajectories of Qt that you obtained in (a) and (b) respectively. (6 Marks) 6. A researcher wants to investigate whether the investment preference is independent of gender. He randomly selects 1000 people and makes the following contingency table: Most Favorite Investment Gender Stock Time Deposit P2P Trust Fund Real Estate Male 90 36 50 120 310 Female 50 63 30 80 171 At α = 0.05, can the researcher conclude that the preference is associated with gender (12 Marks)
VLSI Coursework (CW1) This coursework forms part of the assessment for the Integrated Circuits and Systems module EEEE3098. It must be written as a formal report and submitted via Moodleno later than 3pm on Thursday 12th December 2024. This report is 30% of the overall marks for this module with the usual penalties for late submission. Introduction Very Large Scale Integration design today is carried out totally by use of a computer. The Computer Aided Design (CAD) route for full custom VLSI design is typically as follows: 1. Schematic: System drawn using schematic symbols such as NAND gates, flip-flops etc. 2. High Level System simulated either at the gate or behavioural level Simulation: 3. Cell Design: Individual cells are designed and simulated at the transistor level using SPICE or a similar circuit level simulator. This is called the Pre-layout simulation 4. Cell Layout: CAD layout used to layout individual transistors in each cell - "Polygon pusher" 5. Design Rule Check: The various features drawn are checked for minimum size and separation (DRC) 6. Netlist Extract: Capacitance, resistance and the netlist is now extracted automatically from the layout 7. Electrical Rule Check: The circuit is now checked for electrical violations (ERC), ie outputs short circuit 8. Simulation: The circuit is now re-simulated with SPICE, with the parasitics calculated in (6) above included. This is called the Post layout simulation. 9. System Layout: Complete chip is laid out and if necessary steps 5, 6, 7 and 8 are repeated at the system level. 10. Verification: The layout is converted either to a transistor or agate description. This is then compared with the original schematic description in (1) above. 11. Mask Generation: The layout, usually described in a text form, is then converted into a photomask. One of the standard text layout forms is CIF (Caltech Intermediate Format) Computers today can handle designs with many thousands of transistors. The package being used in this coursework is freeware software. The IC process being used in this coursework is the silicon gate CMOS process and has the following process parameters: Cox = 9 x 10-4 pFµm-2; Cmf = 0.3 x 10-4 pFµm-2 L = 2.00 µm; Cjan/p = 2.0 x 10-4 pFµm-2 KN' = 44 µA V-2; Cp = 0.6 x 10-4 pF µm-2 Kp' = 13 µA V-2; Cjpp/n = ignore Cmp = ignore Aim The aim of this coursework is to: (i) Characterise by computer simulation the transient performance of a previously designed CMOS inverter under both pre- and post-layout conditions. (ii) Provide experience of CMOS layout structures and the associated CAD tools that are used to create and test them, as described above. (iii) Design a CMOS NAND3 gate at the schematic level and produce a valid layout design. (iv) Discuss some important design consideration and latest CMOS technological development. Software Installation Two pieces of software are used for this coursework - Lasi7 and LTspice. These software are available from Moodle and can be run on any Windows computer. Please install them. Note that it is not the aim of this courswork to demonstrate the idiosyncrasies of this CAD packageso I make no apologies for not explaining all the possible commands. Part 1 - Inverter Analysis 1. Cell Design : (Pre-Layout) We shall assume that a CMOS inverter has been designed at the transistor level, pre-layout, such that both transistor widths and lengths are 3.5µm and 2µm, respectively. A pre-layout transistor netlist description for this circuit is provided in the file inverterpre.cir in the folder VLSI_Design. Click LTspice XVII on your desktop and then open the file inverterpre.cir. Examine the file and deduce the meaning of each statement in the netlist. Then do the following and include them in your report: Task 1: Check that the connectivity of the netlist is correct for a CMOS inverter. Do this by drawing the circuit diagram in your report and label the nodes of your diagram with the node numbers and component names from LTspice netlist. [3 marks] Task 2: Verify that the input capacitance of 12.6fF stated in the netlist is correct for the inverter. To do this, calculate the capacitance using an appropriate equation together with the CMOS size and process parameters given in Introduction. [3 marks] Note also that an output capacitance of 100.8fF has been added which represents eight similar inverters loading the output. Note: this value will be changed later on in the coursework design. We need to run a transient analysis which will be used to record the output voltage of the inverter overtime, resulting from the input waveform specified in the net list. To do this click Simulate->Run and then click Plot Settings->Visible Traces to select V(in) and V(out). Task 3: Include the transient plot to your report annotating it to indicate the discharging and charging gate delays τgc and τgd and record the approximate values. [3 marks] Click File->Export data as text to save the transient raw data to inverterpre.txt. They can be examined with any text editor. Use them to achieve a better resolution of delay times. The pre-layout simulation for transient conditions is now complete, but before moving on: Task 4: Check your values of τgc and τgd by calculation and compare these with the results obtained from the spice simulation. [3 marks] 2. Inverter Layout A possible layout for the inverter is presented next and is also printed at the end of this document. To start the CAD software Lasi7, run C:Lasi7Lasi7.exe if you installed Lasi7 in the default folder. You may create a shortcut for Lasi7.exe on your desktop. Click Browse to select the folder VLSI_Design and then select Inverter.cir and then click OK. Click List to bring up a list of available cells. Double click on inverter and then click OK. A coloured layout should appear. Identify the two MOS transistors, the N-well, the Field Oxide etc. If the inverter layout isn’t centred in the screen properly, press “Alt f” . If the layout becomes obscured at any point you can also use “alt f” to refresh the display. If you get in a mess press the ESC key. If this doesn’t fix things then choose Undo along the top. If you still have a problem then you will need tore-copy the VLSI_Design folder. The LASI window is divided into three areas: The drawing window, which is the main area, the button bank on the right and the menu bar. The menus don’t function in the same way as normal menus do – they act as buttons instead. There are actually two banks of buttons available on the right hand side. Clicking on “Menu 1” or “Menu 2” at the top of the bank will change banks, as will clicking the right mouse button in the drawing area. Not all of the buttons actually change function. The function of relevant buttons is explained in the page at the end of this document. Measure the width and length of the transistor within Lasi. The values should be displayed in µm in the bottom left hand corner of the window. Clicking on the button “Grid” will add/remove a grid on the drawing area. The coarseness of the grid can be changed by clicking on “ Dgrid” . 3. Netlist Extraction We now must extract atransistor netlist and parasitics present on the layout. This is carried out with “LasiCkt” . Click “System” in LASI and select “LasiCkt” . Check that the cell for extraction in “Setup” is “inverter” as before and select vlsi.hdr and vlsilab.drc as Header File Name and Footer File Name, respectively. Finally, at the LasiCkt7 menu click “Go” to extract the netlist. Debug any errors you get - there should be none! The net-list is contained in "inverter.cir". Open the net-list with the LTSpice software and note the new value of input and output capacitance. Notice that the input capacitance (16.26fF) is now different from previous one because of it includes additional gate parasitics. Task 5: Using the process data given in Introduction, calculate values for Cin and Cout including additional gate parasitics and compare them with the ones calculated by the software. Use a copy of the inverter layout to highlight the different areas you are considering to compute capacitance values. Ignore the capacitance “C_VDD” between Vdd and Vss (i.e. ground). [6 marks] 4. Simulation of Extracted Circuit (Post-Layout Simulation) Save “Inverterpre.cir” to “Inverterpost.cir” and then update the C_in and C_out with the values from inverter.cir. The extracted net-list with parasitics, Inverterpost.cir, can now be re- simulated in LTspice. Task 6: Include the transient plot to your report as you did before annotating it to indicate the discharging and charging gate delays τgc and τgd and record the approximate values. [3 marks] The delay you just computed are the inherent (unloaded) delays for this inverter cell. We now wish to observe the cell behaviour in response to 8 unit loads and then find the fan-out loading factor τ’LD for this cell (see Lecture 6 – CMOS combinatonal Design for the definition of τ’LD). To do this, modify the inverterpost.cir file, set the output capacitance value Cout to 150fF and then run again the transient analysis. The 150fF is approximately equivalent to 8 unit loads plus the inherent output capacitance,i.e. 19.6fF + 8 x 16.26fF ≈ 150fF You will see that the output doesn't quite reach Vdd before it starts falling again, so change the clock by editing the spice netlist. In the netlist file, find the line near the top that describes V2 via the PULSE statement. Change the 5ns to 10ns and the 10ns to 20ns – this halves the clock rate. Change the transient simulation time from 10ns to 20ns and then re-run the transient analysis. Task 7: Include the transient plot to your report also for the loaded case. Measure the new τgc and τgd to a suitable accuracy. [3 marks] Task 8: As did before, compute the delays τgc and τgd for the post-layout inverter in both loaded and unloaded case. [6 marks] Task 9: Compare the calculated values with the one obtained in simulation and give possible reasons why the values do not fully agree. Show how improvements can be made to the simulation, calculation or both, to obtain a better agreement. [4 marks] Task 10: Determine τ’LD in units of ns/pF for both L -> H and H -> L. [2 marks] Task 11: Why is the propagation delay L -> H greater than the propagation H -> L even though the transistors are of the same size? [3 marks] Part 2 - NAND3 Design and Layout The purpose of this section is to give you a different viewpoint of layout design. Rather than just analysing existing designs, as we have done in lectures, you are here to try to design your own circuit and create the corresponding layout – taking design rules into account, of course. I hope that you will get a better understanding of how the layers fit together to make devices and circuits, as well as the related skills like circuit design and design rules. The aim is the schematic and layout design of a digital logic cell to be used as a standard cell of height 60λ . Please note that as already mentioned, the design must be free of design rule errors. You should also try to make it as compact as possible. When marking the layouts consideration will be made of the tidiness of the design. The gate you will be designing is a NAND3 (3 input NAND gate). Schematic Design The specification you must meet with your design is that the worst case switching delay must be less than 2ns when driving a load of 100fF. You must design both the P and N networks intelligently, which is to say that you must ensure that the values for τgc and τgd meet the timing requirement, but that they are also not over engineered. Do not exceed the timing specification by more than a factor of 20%, i.e. your τgc and τgd values must be greater than 1.6ns,but do not need to be identical. You should calculate the width and length for each transistor. Task 12: In your report, draw the NAND3 schematic circuit diagram. [5 marks] Task 13: Show your complete calculations the width and length for each transistor to demonstrate your design respects the requirements. [20 marks] Layout Design Now you have designed your circuit, you need to start drawing the layout. Run Lasi7. Instead of selecting an existing cell, type the name of your new cell and press OK. A new window will ask you to select the cell Rank. Choose 2 and press OK. Firstly, add the stdcell_60 cell to your design. This includes a small amount of metal that shows where the Vdd and Vss lines should go. You should extend this metal in the x direction to the final width of your cell. To add the cell, click the Obj button and choose the stdcell_60 cell from the list. Now click Add and click to add the cell. To change back to being able to add rectangles, click Obj and select Box, before using Add again. You should now start to draw your gate. You can choose what layer to draw by pressing the Layr button in the button bank on the right. Once you have done this, click Add and you can then draw rectangles of that layer. Please note that the snap grid resolution is 0.5λ . Start by drawing the device and polysilicon layers, ensuring the width and length of the overlap (i.e. the gate) are correct. Deleting a rectangle Click aPut to deselect everything, click fGet (full get) and click and then click again on the layout window to draw a box around one of the corners of the rectangle you wish to delete. It should turn white. Now click Del. Resizing a rectangle Click on aPut to deselect everything. Now click on the Get button. Draw a box around the edge of the rectangle you wish to resize. That single edge should turn white. Now click Mov, the click at the start point of the move, move the mouse and click on the destination. Moving a rectangle Use Get orfGet to select the entire rectangle and then use Mov as above to move the whole rectangle. DRC Once you have finished the layout of your gate you should run DRC to check it is valid. Click the System menu, then LasiDrc. In the LasiDrc window, click Setup to ensure that the cell name is correct and select vlsilab.drc from the folder VLSI_Design as DRC File Name. Next make sure that “Start check” is 1, and “Finish check” is 100. You should also always click “Fit” to ensure that the DRC tool looks at the smallest complete area possible. Once the DRC has run (click Go), you should get a message about any errors. If you have any, you can open the DRC error map file using the Map menu from LasiDRC. Post Layout Check Task 14: After you have completed your layout, make an estimate of the output capacitance of your layout design. Your estimate should include the junction capacitance only, there is no need to add the wire capacitance. Include your calculations in your report. Does your design still meet the required timing? If not, please modify the design to meet the requirements. [15 marks] Part 3 - Discussion Task 15: Discuss the design solutions if the NAND gate needs to drive a 100pF external load while still meeting the delay requirements. [6 marks] Task 16: Why delay, power consumption and area are the most important IC design parameters, in terms of environmental impact and commercial market? How are they related to each other, in terms of design consideration? [6 marks] Task 17: How to mitigate the design risk, in terms of Layout design rule settings? [3 marks] Task 18: FinFET is widely used in modern chip designs. What are its advantages and disadvantages? [6 marks] Final Steps You should include a good quality screen capture (not photograph!) of the complete design in your report and make sure your report covers all the tasks. You should also create a zip of the VLSI_Design folder and submit that alongside your report, so that I can verify the files myself. Please note that missing design files will result in lost marks, so take care to include all of the files you have produced. Report guidelines Report must not exceed 12 pages. Please use Microsoft Word or an equivalent software to write it, including equations. Do not put hand-written parts. Also schematic and diagram have to be drawn with a software of your choice. Please include the task number in your report to facilitate marking. The usual deduction will apply for work submitted late. Do not leave your submission to the last minute, even a few seconds late will incur the late penalty. Plagiarism and collusion are actively checked for. Please do not allow anyone else access to your work, even your friends.
Econ2Z03 Sample Exam Questions_Ch8,9,10 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1. A city is considering a proposal to award an exclusive contract to Clear Vision, Inc., a cable television carrier. As the single supplier of cable television services, the company faces the following demand and marginal cost functions: P = 28 - 0.0008Q MC = 0.0012Q, where Q = the number of cable subscribers and P = the price of basic monthly cable service. What quantity would be expected? A) 12,000 B) 14,000 C) 10,000 D) 11,000 2. Which of following is an example of a homogeneous product? A) Gasoline B) Copper C) Personal computers D) Winter parkas E) both A and B 3. At the profit-maximizing level of output, what is relationship between the total revenue (TR) and total cost (TC) curves? A) They must be tangent to each other. B) They must have the same slope. C) They must intersect, with TC cutting TR from above. D) They must intersect, with TC cutting TR from below. E) They cannot be tangent to each other. 4. The demand curve facing a perfectly competitive firm is A) the same as its average revenue curve, but not the same as its marginal revenue curve. B) not defined in terms of average or marginal revenue. C) the same as its average revenue curve and its marginal revenue curve. D) not the same as either its marginal revenue curve or its average revenue curve. E) the same as its marginal revenue curve, but not its average revenue curve. Consider the following diagram where a perfectly competitive firm faces a price of $40. Figure 8.1 5. Refer to Figure 8.1. At the profit-maximizing level of output, ATC is A) $31. B) $30. C) $44. D) $40. E) $26. 6. Bette's Breakfast, a perfectly competitive eatery, sells its "Breakfast Special" (the only item on the menu) for $5.00. The costs of waiters, cooks, power, food etc. average out to $3.95 per meal; the costs of the lease, insurance and other such expenses average out to $1.25 per meal. Bette should A) raise her prices above the perfectly competitive level. B) continue producing in the short and long run. C) lower her output. D) close her doors immediately. E) continue producing in the short run, but plan to go out of business in the long run. 7. Consider the following statements when answering this question I. Increases in the demand for a good, which is produced by a competitive industry, will raise the short-run market price. II. Increases in the demand for a good, which is produced by a competitive industry, will raise the long-run market price. A) I is false, and II is true. B) I and II are true. C) I is true, and II is false. D) I and II are false. Figure 8.2 8. Refer to Figure 8.2. If the firm expects $80 to be the long-run price, how many units of output will it plan to produce in the long run? A) 34 B) 22 C) 64 D) 50 E) 38 9. In long-run competitive equilibrium, a firm that owns factors of production will have an A) economic profit = $0 and accounting profit > $0. B) economic and accounting profit can take any value. C) economic and accounting profit > $0. D) economic and accounting profit = $0. E) economic profit > $0 and accounting profit = $0. Figure 9.2 10. Refer to Figure 9.2. At price 0H and quantity Q1, consumer surplus is the area A) 0FGQ1. B) HFGB. C) EFC. D) EDGF. E) none of the above 11. Under a binding price ceiling, what does the change in consumer surplus represent? A) The loss in surplus for those buyers who previously purchased some units of the good at the higher price, but these units are no longer produced at the lower price. B) The gain in surplus for those buyers who can still purchase the product at the lower price. C) The loss in surplus for those buyers who would like the purchase the excess demand created by the price ceiling policy. D) Both A and B are correct. E) Both A and C are correct. 12. Having seen the quantity of drugs supplied by pharmaceutical companies in a competitive market, a government decides to force companies to sell exactly the same quantity of drugs at prevailing market prices. The government then forbids additional drug sales and allows doctors to prescribe the drugs at no cost to patients in need. This government scheme is A) efficient as the quantity of drugs traded is the same as under a free market. B) efficient as consumer surplus is maximized. C) likely to be inefficient as doctors are unlikely to prescribe drugs to the consumers who are willing to pay the most for the drugs. D) likely to be inefficient as drug producers have a captive buyer. E) efficient as the price of drugs paid by the government is the same as under a free market. 13. The market supply curve for music downloads is Q = 135(P-1) where Q is millions of downloads and P is the price in dollars per track. If the current price is $1.20 per download, what is the change in producer surplus if the price increases by $0.20 per track? A) $10.8 million B) $5.4 million C) $27 million D) $8.1 million Figure 9.4 14. Suppose the market in Figure 9.4 is currently in equilibrium. If the government establishes a price floor of $40, consumer surplus will A) fall by $350. B) remain the same. C) fall by $50. D) rise by $50. E) rise by $350. Figure 9.7 15. Refer to Figure 9.7. Because of the policy, consumer surplus fell by A) $45,000. B) $10. C) $12,500. D) $25,000. E) $20. 16. A specific tax will be imposed on a good. The supply and demand curves for the good are shown in the diagram below. Given this information, the burden of the tax: A) falls mostly on consumers. B) is shared about evenly between consumers and producers. C) falls mostly on producers. D) cannot be determined without more information on the price elasticities of supply and demand. 17. What is the welfare impact of a subsidy policy? A) Producer surplus increases, consumer surplus declines, and total welfare increases due to the subsidy program. B) Producer and consumer surplus increase, and these gains are smaller than the government cost. C) Producer and consumer surplus increase, and these gains are larger than the government cost. D) Producer surplus increases, consumer surplus declines, and total welfare declines. 18. When the demand curve is downward sloping, marginal revenue is A) equal to price. B) more than price. C) equal to average revenue. D) less than price. 19. For the monopolist shown below, the profit maximizing level of output is: A) Q3. B) Q2. C) Q5. D) Q1. E) Q4. 20. Which of the following is NOT true regarding monopoly? A) Monopoly price is determined from the demand curve. B) Monopolist can charge as high a price as it likes. C) Monopoly is the sole producer in the market. D) Monopoly demand curve is downward sloping. 21. Compared to the equilibrium price and quantity sold in a competitive market, a monopolist will charge a price and sell a quantity. A) higher; smaller B) lower; larger C) higher; larger D) lower; smaller E) none of these 22. Suppose that a firm can produce its output at either of two plants. If profits are maximized, which of the following statements is true? A) The marginal cost at the two plants must be equal. B) The marginal cost at the second plant must equal marginal revenue. C) The marginal cost at the first plant must equal marginal revenue. D) all of the above E) none of the above 23. A monopolist has set her level of output to maximize profit. The firm's marginal revenue is $20, and the price elasticity of demand is -2.0. The firm's profit maximizing price is approximately: A) $0 B) $40 C) $20 D) $10 E) This problem cannot be answered without knowing the marginal cost. 24. For a monopolist, at the profit-maximizing level of output, demand is A) unit elastic. B) elastic, but not infinitely elastic. C) infinitely elastic. D) completely inelastic. E) inelastic, but not completely inelastic. 25. The demand curve for red herrings is: Q = 250 - 5P What level of output maximizes revenue? A) 85 B) 45 C) 125 D) 0 E) 245 26. The more elastic the demand facing a firm, A) the higher the value of the Lerner index. B) the higher its profit. C) the lower the value of the Lerner index. D) the more monopoly power it has. 27. Roaring Lion Studios can produce DVDs at a constant marginal cost of $5 per disk, and the studio has just releasing the DVD for its latest hit film, Ernest Goes to the Hamptons. The retail price of the DVD is $25, and the elasticity of demand for this film is -2. Has the studio selected the profit-maximizing retail price for this DVD? A) No, the retail price is too low B) No, the retail price is too high C) Yes D) We do not have enough information to answer this question. 28. A manufacturer of digital music players uses a proprietary file format that is not used by the other firms in the market. This action by the firm maybe an example of using a to reduce the number of firms in the market and to maintain a relatively inelastic demand for its products. A) positive externality B) natural monopoly C) barrier to entry D) subsidy 29. Unlike a competitive buyer, A) a monopsonist pays a different price for each unit purchased. B) a monopsonist pays a price that depends on the number of units purchased. C) a monopsonist faces an upward-sloping industry supply curve. D) a monopsonist sets marginal value equal to marginal expenditure. Figure 10.5.1 The marginal value curve and expenditure curves in the diagram above are those of a monopsony. 30. Refer to Figure 10.5.1. What quantity will be purchased in a competitive market? A) Q1 B) Q2 C) Q3 D) Q4 E) none of the above
FACULTY OF ECONOMICS AND MANAGEMENT EPPA1013: PRINCIPLES OF ACCOUNTING SEMESTER I SESSION 2024/2025 PROJECT: FINANCIAL STATEMENT FOR SERVICE OPERATIONS This project is a business process simulation that contributes 20 marks to the overall assessment for this course. It aims to enhance students' understanding and practical knowledge of different business types and ownership forms, the recording process, and the preparation of financial statements. This is a group project, with each group consisting of five (5) members. Each group must create a sole proprietorship (simulation only) that will operate a service business for 3 months, from 1 October 2024 to 31 December 2024. In the setup phase, students will register the business, design the logo and business source documents, and plan the business activities, mission, and vision. During the operation phase, each business will conduct transactions, some of which will involve interaction with other student groups' businesses. Transactions will be recorded in journals and ledgers. In the final phase, each business will prepare financial statements and closing entries. PART A: GENERAL INSTRUCTIONS 1. The group consists of 5 (five) members 2. Each group must determine the type of service business they want to operate. Examples of service business types include: i. Advertising ii. Delivery iii. Photocopying iv. Accounting Firm v. Salon vi. Consultancy/ Advisory Services 3. Each group must also decide on the name of the business they will operate. The business name must be registered by completing the Business Registration Form. (Form. A) and the Business Name Approval Form (Form PNA.42), which can be downloaded from the Companies Commission of Malaysia (SSM) website. 4. The business established must be a sole proprietorship. PART B: PROJECT IMPLEMENTATION The detailed activities for the project implementation are as follows: WEEK ACTIVITY LEARNING OUTCOMES* 1 & 2 Form groups of five members - 3 o To register your business (simulation only), each group needs to: • download Form. A and Form. PNA42 from the Companies Commission of Malaysia website, • fill out the forms. o In this activity, each group must also provide the following information: • Business name (as registered with SSM), • Business logo, • Main business activity, • Mission, and Vision of the business 1 4 Design source documents that will be used in your business transactions. Examples of source documents include: • official receipts, • sales invoices, • payment vouchers. 1 5 Conduct at least 30 transactions for the first three months of the business: • Each transaction must have a source document and be recorded. • These 30 transactions should consist of 10 transactions with other groups and 20 transactions not involving other groups (e.g., paying employee salaries). You may use the space on UKMFOLIO or WhatsApp groups to communicate with other group members. • Analyze each transaction using the accounting equation. 1 & 3 6 Using the transactions that have been made: • Record journal entries for each transaction, • Open all relevant accounts, • Post all journal entries, • Prepare atrial balance. 2 & 3 7 o Prepare at least 5 adjustment entries, • Record adjustment entries, • Post adjustment entries, o Prepare an adjusted trial balance. 2 & 3 8 o Prepare financial statements, o Record closing entries, o Prepare a post-closing trial balance. 2 & 3 LEARNING OUTCOMES*: 1. Identify accounting concepts and principles in business. 2. Solve the steps of a complete accounting cycle in financial statements generation. 3. Practice ethical behaviour in accounting information selection. PART C: PROJECT REPORT SUBMISSION The complete results of the project, including the prepared financial statements, must be submitted in soft copy (Word document/PDF file) via UKMFolio by the group leader no later than the 15th week of the lecture session, specifically by Monday, 20 January 2025, at 11:59 p.m. Early submissions are encouraged. The project assessment weight is 20%, with 15% evaluated based on the project report submitted by the students (group marks) and the remaining 5% through peer evaluation within the group (individual marks).
