Semester Two 2024 Mock Exam Faculty of Engineering EXAM CODES: CIV2242 TITLE OF PAPER: GEOMECHANICS 1 EXAM DURATION: 50 minutes writing time READING TIME: 10 minutes (30 mins scan/upload time) Question 1 (8 marks) A new playground is proposed to build in Monash University and preliminary site investigations were carried out by a geotechnical company. A soil sample from the proposed area was collected and tested in the laboratory. The following results were found from the laboratory experiments. Porosity (n) = 0.3; Specific gravity of the soil solids (Gs) = 2.7; and moisture content (w) = 10% The density of water is 1000 kg/m3 (a) Calculate the bulk density of the soil sample (3 marks) (b) Calculate the saturated density of the soil sample (3 marks) (c) Determine the mass of water to be adder to 10m3 of soil for full saturation (2 marks) Question 2 (15 marks) The following are the results of consolidated-undrained triaxial tests on undisturbed soils retrieved from a 4-m-thick saturated clay layer in the field (γsat = 19 kN/m3, γw = 9.81 kN/m3). In the first stage, the drainage valve was opened to allow water to drain under the applied cell pressure, so that excess pore water pressure developed during the first stage was fully dissipated. In the second stage, the drainage valve was closed and the axial load was increased. Given the following triaxial test data at failure; Answer the following questions by plotting Mohr’s circle of stresses on a graph paper. Attach your graph paper along with your answer sheet. (a) Draw and clearly label the effective stress Mohr’s Circles at the failure. (8 marks) (b) Determine the effective shear strength parameters. (2 marks) (c) Estimate the compressive strength of the sample if it were tested in anunconfined situation. (3 marks) (d) Estimate the shear strength in the middle of the clay layer. (2 marks) Question 3 (12 marks) Figure 1 presents the ground profile of a construction site intended for a multistorey building. It has three layers, each differing in height and hydraulic conductivity. H 1=2m, H2=2.5m, H3=3m, k1= 3x10-4cm/s, k2= 2x10-2cm/s,and k3= 5x10-5cm/s. Figure 1:Ground profile (a) Determine the equivalent hydraulic conductivity for vertical flow. (5 marks) (b) Determine the equivalent hydraulic conductivity for horizontal flow. (5 marks) (c) Compute the ratio of equivalent hydraulic conductivity for horizontal flow to vertical flow. Discuss the concept of seepage and hydraulic conductivity. (2 marks) Question 4 (15 marks) The Metro Tunnel is the first step towards a 'metro-style' rail network for Melbourne with the 'turn up and go' train services that are the hallmark of the world's great cities such as London, New York, Hong Kong and Singapore. This project consists of twin nine-kilometre tunnels, which will deliver a new dedicated pathway through the heart of the city for Melbourne's busiest rail lines. The tunnel will be constructed under the Yarra River. The cross section shown in Figure 2 is taken through part of Melbourne along the centre line of a proposed rail tunnel. Please answer the following questions related to this cross section. Figure 2. Cross section along the centre line of a proposed tunnel (a) Name the oldest geological unit shown in the cross section. (2 marks) (b) For the geological unit you have selected as the oldest, describe its material, mass and geomorphological properties. (3 marks) (c) In order to maintain suitable gradients, the 6 m diameter TBM tunnel must pass through this section between elevations of -14 m and -20 m. List 3 geotechnical issues that you would need to consider for a tunnel at this elevation. (6 marks) (d) For construction,a concrete batching plant will need to be constructed on the ground surface on the south side of the Yarra River (between Ch 220 m and 450 m). The batching plant will occupy an area of 50 m by 50 m and is expected to apply 200 kPa. Describe the possible ground response due to the loading applied. (4 marks)
Module Title Principles of Marketing Assignment Mode Group Project Word Count Limit 2500 words (+/- 10%) Citation Format APA Marks 40 marks Report Topic A group of 4-5 students will prepare a marketing report focusing on the marketing strategy and marketing mix for an innovative product or service to be launched for a real- world organisation. References You are required to consult and fully reference a MINIMUM of 10 different sources of information Overall Rationale for the PMKT Assessments Influenced by the key skills and attributes of the working marketer, Principles of Marketing requires you, the student, to form. a working project group composing diverse skills sets and work on the Marketing Plan for a product from the first to the last session starting with small presentations and culminating in a Report and Major Presentation, following the Marketing Process. Students are expected to assume they are working as marketing consultants. Working in groups of 4-5 members, you will choose a company/brand/product on which to conduct marketing research and analysis for the entirety of the module, culminating in a Major Report (Assessment 2, worth 40% of your overall mark for the module) and a Major Presentation (Assessment 3, worth 40%). To help you on this journey, you are to deliver smaller (ungraded) in-class group presentations meaning your group will commence this process from Session 1 and hone your research, communication and group skills over the whole semester. Assignment Brief Influenced by the key skills and attributes of the working marketer, Principles of Marketing requires you, the student, to work on a Marketing Plan for a chosen company. You will develop an innovative product/service for a company of your choice which operates within the consumer electronics industry. Your forward-looking written report must be based on credible research describing the recommended marketing activities for the chosen company in relation to the innovative product/service. Your report will include a detailed explanation of the following sections: Introduction: Company, Brand and Product (10 marks) The introduction should describe the chosen company very clearly, summarising or paraphrasing to show understanding. This section should be accurate and up to date as of 2022. The key attributes of the innovative product/service must be introduced here. Marketing Strategy (S,T, D and P) and Recommendations (10 marks) This section outlines the proposed segmentation, targeting, differentiation and positioning of the innovative product/service and should be forward looking. Target market segments should be clearly defined. The product should be clearly differentiated from its competitors and a positioning statement must be recommended. Marketing Mix (the 4 P’s) and Recommendations (10 marks) This section outlines the recommended Mix – Product, Place, Price and Promotion - for the innovative product/service. Product branding, packaging, labelling and support (augmented) services should be succinctly and clearly described. A recommendation on strategy for sustaining the product life is well made. Channel types and levels need to be described with a clear diagram. A recommendation on a more effective channel shows relationship of product to market to channel. The pricing strategy (one of the 5 main) is to be defined with examples. Promotion analysis use examples to outline the Theme and Appeal of future promotions. APA Referencing (10 marks) This group assignment is a combination of theory and practical application of key concepts relating to the module on Principles of Marketing. The required report must provide evidence of wider research and be adequately presented, investigated, and argued in a logical and coherent manner. Appropriate conclusions made must be explained, justified and appropriately referenced as is expected of a report at this level of study. The report further requires a MINIMUM of 10 different sources of information (most assignments achieving the top two grade levels available include 10 references). You must use the APA Referencing system to acknowledge your sources of information (both in-text, and as a reference list at the end). ONE member of the group must upload the assignment to the Kaplan Canvas site by the due date. Further information on the structure of the report and other details of the assignment will be shared by the lecturer during the conduct of the sessions.
[COM00052H] BEng, BSc, MEng, MMath and MSc Degrees 2024–25 Open Assessment Department Computer Science Module Autonomous Robotic Systems Engineering (AURO) Title Individual coursework Issued: Monday 04/11/2024 Submission due: 12 noon, Monday 13/01/2025 Feedback and Marks due: Monday 17/02/2025 Word limit 2000 words for the report Allocation of Marks 40% allocated to implementation and 60% to the report Instructions All students should submit their answers through the appropriate VLE submission point in the Assessment area of the VLE site by 12:00 noon on Monday, 13/01/2025. An assessment submitted after this deadline will be marked initially as if it had been handed in on time, but the Board of Examiners will normally apply a lateness penalty. Your attention is drawn to the section about Academic Misconduct in your Departmental Handbook . Any queries you may have on this assessment should be posted on the Discussion Board on the Virtual Learning Environment (VLE) page for Autonomous Robotic Systems Engineering (AURO) in the appropriate discussion area. No questions will be answered after 23/12/2024. 1. Task definition This assessment focuses on the retrieval of items by autonomous mobile robot(s). You will be provided with a simulated world containing items of different types distributed throughout the environment, which the robot(s) must collect and deposit in the appropriate zone(s). This simulated world will also contain obstacles that the robot(s) need to avoid. A robot can collect an item by driving into it and using a functionality to collect it, and will ‘ hold’ the item until it uses another functionality to offload the item. Once an item has been collected and successfully returned to a zone, a new one will automatically spawn to replace it. You must design and implement a solution to this task, using mobile robot(s) that autonomously collect the items and return them to the appropriate zone(s) in an efficient manner. 2. Deliverables This assessment is worth 100% of the module mark, and is made up of 2 parts with the following weightings: 1. Implementation: 40% 2. Report: 60% Guidance on what you are required to do for each part of the assessment is provided in the following sub-sections. 2.1 Implementation (40%) You should engineer an autonomous robotic system that solves the assessment task efficiently, while obeying the following constraints: ● You must implement your solution in simulation, using the Robot Operating System (ROS). Specifically, you must use ROS 2 Humble Hawksbill, Gazebo Classic 11, and the Python client library rlcpy. ● You must use autonomously controlled (i.e. not teleoperated) TurtleBot3 Waffle Pi robot(s). Your solution may use up to 3 robot(s). ● You must include a README file that describes how to run your code, and details any packages or environment variables that your implementation depends on. It should also detail what scenarios your implementation should be exercised on, including values used to configure nodes and launch files as appropriate. There are many different ways of approaching the assessment task, so there is scope for a variety of solutions. Your implementation will be assessed against the following criteria: How effectively the task is achieved [25 marks]: You will be assessed on the intelligence of your autonomous robotic system, and how effectively it addresses different aspects of the task. Multi-robot systems may be more sophisticated and perform. the task more efficiently, but only if they are implemented appropriately. Marks will be awarded per the following criteria. ● Appropriateness of the obstacle avoidance solution [5 marks] ● Effectiveness of the search strategy [5 marks]. At most [3 marks] for a single robot solution. ● Effectiveness of the collection strategy [5 marks]. At most [3 marks] for a single robot solution. ● Efficiency of the task and how correctly it achieves the goals [10 marks]. At most [6 marks] for a single robot solution. Use of concepts and comments [10 marks]: You will be assessed on the modularity of your solution and on the breadth of the ROS features that your implementation uses, and how well you have demonstrated your understanding of them (through correct usage). Your implementation should be easy to understand. You will be assessed on the structure of your code, the use of sensible naming conventions and comments, and how comprehensive your README file is. Marks will be awarded per the following split. ● Architecture [5 marks] ● Modularity [5 marks] Provision of specific scenarios for running your solution [5 marks]: The instructions for running your solution should specify the simulation scenarios you specifically considered when designing your solution, including the parameters of launch files and or nodes. You will be assessed on how well the provided scenarios exercise your solution. Marks will be awarded per the following criteria. ● At most 1 mark per valid scenario. Diversity of scenarios will be taken into account. You will be provided with code that defines the assessment task, which should be downloaded from the VLE. This code sets up the simulated world, and runs a ROS node that spawns items and keeps track of when they are collected and returned to the appropriate zone(s) by the robot(s). You will also be provided with a ROS node that processes images from a robot’s camera, and publishes information about any items that are detected. You must use this code without modification, as it defines the assessment parameters of the task. You are allowed to use any of the example code provided as part of the teaching delivery for the AURO module, including solutions to practical exercises. The use of 3rd party packages is also permitted, as long as you cite the original source and include instructions on how to build them. Note that a solution that does not build correctly may be awarded 0 marks. 2.2 Report (60%) You must write a report that details the design and implementation of your solution. You should describe the design of your solution, analyse the performance of your solution, and present the results in your report. Finally, your report should evaluate the strengths and weaknesses of your solution, and reflect on related safety implications and ethical considerations. The report must be structured as follows: 1. Overview [5 marks]: This section should describe at a high-level what methodology you used in your solution. You should explain what influenced your approach to solve the given problem [200 words]. Marks will be awarded for a concise description. 2. Architecture [13 marks]: This section should have a diagram illustrating the high-level architecture and a description of the architecture using the diagram. You should identify the nodes responsible for implementing the control strategy adopted [300 words]. Marks will be awarded per the following criteria. ● Appropriateness of the diagram [3 marks] ● Depth, breadth and clarity of the discussion of the chosen diagram [5 marks] ● Correct identification and description of nodes [5 marks] 3. Control [12 marks]: In this section, you should provide RoboChart state machines for the control nodes identified in Section 2 on Architecture. You should explain the state machines used [300 words]. Marks will be awarded per the following criteria. ● Appropriateness of the control architecture used for the task [4 marks] ● Depth, breadth and clarity of the description of the machines used [4 marks] ● Demonstrated understanding of the design and its behaviour [4 marks] 4. Evaluation [10 marks]: In this section, you should provide an evaluation of your solution through one or more methodologies, for example, simulation, complexity analysis, data analysis, descriptive, experimental [600 words]. ● At most 3 marks will be awarded per chosen evaluation method [9 marks] ● Justification of the chosen evaluation methods [1 mark] 5. Safety and ethics [10 marks]: This section should include a discussion of the ethical and safety implications of the problem and your solution in particular. You should also reflect on how these topics would relate to your solution’s approach, if it were implemented in a real-world scenario [300 words]. ● Identification of ethical and safety implications [3 marks] ● Depth, breadth and clarity of the discussion on the implications [3 marks] ● Demonstrated understanding of the implications for real-world scenarios [4 marks] 6. Simulation scenario [5 marks]: This section should include screenshot(s) of the simulation and explain and reflect on the overall strategy you have implemented. You should justify the choice of simulation scenarios [300 words]. The remaining [5 marks] of the report mark will be based on its presentation (structure, figures, adherence to the structure, and use of referencing). Your report should be formatted using A4 paper size, with a minimum font size of 12pt and minimum margins of at least 2cm, and any references should follow the IEEE referencing style1. The report must not exceed the word limit of 2000 words (excluding references). If your report exceeds this word limit, the marker will stop reading when they reach the limit, and base the mark on what they have read so far. There is no limit on the number of images. 3. Submission The submission of your implementation and report for this assessment should abide by the following rules. 3.1 Anonymity Your name, username, email address, exam number or any other identifying information must not be present anywhere in your submission. This includes all ROS package metadata, code comments, environment variables, Linux terminal prompts, PDF metadata, etc. You must not include any images that could deanonymize your submission. 3.2 Electronic submission You should submit your deliverables via the submission point on the VLE as two separate files: your report should be submitted as a PDF file, and your implementation should be submitted as a single ZIP file. The contents of the ZIP file should be structured as shown in Figure 1. submission.zip |── README.txt |── rosgraph.png |── src L─── Your ROS packages Figure 1 : Required structure of electronic submission ZIP file. The source code of your implementation should be included in a directory called src containing your ROS packages. You should not include your entire ROS workspace – i.e. you should exclude the build, install, and log directories created by col con. Your README file should be in plain text format. You should also include a PNG file exported from rqt_graph in a file named rosgraph.png that shows the ROS graph of your solution. Your report must be a single PDF file. It is your responsibility to ensure that your implementation runs under the ROS 2 Linux environment provided to you as part of AURO before submission.
Project 1: Combining Data from Multiple Sources Introduction Finance research often requires assembling a data set from different sources. In many cases, the source data is not formatted such that it can be imported easily into Python for analysis. This assessment helps you develop the foundational skills of data acquisition, cleaning, and merging. You will combine stock price information distributed across many files and produce the output as a JSON file. We ask you to write general code, such that it can adapt easily to different file formats. Writing general code can be a daunting exercise at first. However, it is in your best interest to practice writing functions that can adapt to different configurations. Doing so makes your code more robust, easier to maintain, and upgradeable. To help you, we have provided a Python scaffold. This file, called zid_project1 .py contains all the functions needed for this project. Each function has a detailed docstring describing what the function does, the input parameters, and the object it returns. The remainder of this document provide information on: • The data files you will receive. • Instructions to set up your development environment in PyCharm. • Detailed step-by-step instructions required to complete the assessment. Please follow these instructions closely. Our ability to evaluate your work requires that you do so. You should develop your code within PyCharm. Submission, however, will be through Ed. You will only need to copy your zid_project1.py file into Ed. Unlike the code challenges you have done so far, Ed will not provide you any feedback on your code. You can still submit multiple times before the deadline – Only your final submission on Ed will be marked. The Source Files All required files are included in a zip folder with the following structure: project1/ | project_desc.pdf | README.txt | TICEKRS.txt | zid_project1.py
Empirical Finance Spring II 2022 Assignment 1 Data are from the Center for Research in Security Prices (CRSP). The two monthly series from CRSP are the value-weighted with-, RNt, and without-dividend nominal returns, RXt, of CRSP stock market indexes (NYSE/AMEX/NASDAQ/ARCA). The sample period is from 1946:M1 to 2020:M12. The monthly nominal dividend series are constructed as follows. • A normalized nominal value-weighted price series is produced by initializing P0 = 1 and recursively setting Pt = (1 + RXt)Pt-1, • A normalized nominal dividend series, Dt, is obtained by recognizing that Dt = (RNt − RXt)Pt-1 . You will find “dividends.xlsx” that explains how to construct Pt (Price) and Dt (Div). Q1. (70pts) Constructing dividend growth rates and log pd ratio 1. (10pts) Compute log dividend growth rates, Ad= In(D/Dt-1), and plot Ad. 2. (10pts) Compute the sample average and standard deviation of Ad in the range between 1947:M1 and 2020:M12. 3. (20pts*) Discuss the time series properties of △d. 4. (10pts) Aggregate the monthly dividends Dat = Σi11=o Dt-i. It is important to understand that for each December, we are aggregating the 12-months of dividends. Thus, T runs in annual frequency (i.e., December of each year) while t runs in monthly frequency. Compute the annual log growth rates Adta = In(D/Dat-1) and provide its sample average and standard deviation. 5. (10pts*) Plot the time series of Ad and compare with Ad (you could evenly distributeAd over the 12 months). Discuss the sample standard deviation of the two series. 6. (10pts) Consider the December value of price P as P. Therefore, the length of time series of P matches that of D. Construct the log pd ratio pd- = In(P/D) and compute its sample average and standard deviation in the range of 1948 to 2020. Q2. (60pts) Predictability 1. (20pts) Run the following OLS regression ∆dτ+h = αh + βhpdτ+ τ+h (1) for h ∈ { 1, 2, 3, 4, 5} using the most available sample. For example, ∆dτ+5 is available from 1953 to 2020 whereas pdτ is available from 1948 to 2015. Report the estimate of βh and the implied R2 value for each h. Q3. (20pts) Reading on dividend/return predictability Read Binsbergen and Koijen (2010) and summarize the paper. The summary should be not more than two paragraphs Q4. (50 pts) Correlation between stock and bond returns You will find "returns.csv" that includes two daily series of stock returns and bond returns (of maturity 1-year) which range from 1971 to 2020. 1. (20pts) Compute the rolling correlation between stock returns and bond returns bysetting window interval to w. That is, you are to compute corr(R, Ro,) for each t where 2/w + 1 ≤ t ≤ T - 2/w Plot the time series of rolling correlation for w=60 and =900. 2. (30pts*) Describe the correlation pattern and provide potential explanations. (Hint:feel free to search online). The explanation should be not more than two paragraphs.
Managing Sustainability in Global Value Chains (N1658) Coursework report: Company Reporting and Modern Slavery 1. Aim The coursework report for Managing Sustainability in Global Value Chains is designed to allow you to evaluate one of the main mechanisms established by the UK government for businesses to report on the social sustainability of their global value chains. The Modern Slavery Act in the UK was established in 2015 and obligates businesses “to report annually on the efforts they have undertaken to identify, prevent, and address modern slavery in their supply chain” (Voss et al (2019: 62-63). The coursework report will focus on two key activities: (a) your assessment of the content and coverage of a sample of company reports in a sector and value chain of your choice which have been submitted under the Modern Slavery Act, and (b) your evaluation of the effectiveness of the reported statements, their limits in dealing with modern slavery in global value chains, and what businesses might do to improve social sustainability. The coursework report accounts for 30% of your module mark for N1658. 2. Learning objectives The coursework report will allow you to address two of the modules learning objectives: LO2: “make appropriate use of frameworks and examples to analyse global value chain sustainability processes and programmes” LO3: “Critically evaluate the management challenges in the relationship between social … sustainability and global value chains” (LO3). 3. Approach In developing and producing your coursework report a number of steps should be followed: (a) Select one main sector that interests you to investigate from the UK government’s online database of Modern Slavery statements (the Modern Slavery Statement Registry) at https://modern-slavery-statement-registry.service.gov.uk/. The Registry site is here: The search function looks like this (click on ‘use search filters’): You are then taken to a list of search options: (b) Choose one year between 2020 and 2022 and the size of the company reporting. In order to narrow the search down I suggest you either choose companies over £500 million turnover, or select some larger and some smaller companies for comparison. (c) Choose a sector with activity normally associated with global value chains (see notes below). The sectors listed are: • Automotive, machinery and heavy electrical equipment (possible) • Charitable / not-for-profit activities (unlikely) • Cleaning and security services (unlikely) • Construction, civil engineering and building products (unlikely) • Consumer services, including accommodation, hospitality, tourism and leisure (possible) • Cosmetics and toiletries (possible) • Defence and aerospace (likely) • Durable consumer goods, including electronics and appliances, home furnishings and other accessories (likely) • Education and research (unlikely) • Fashion, textiles, apparel and luxury goods (likely) • Financial, insurance and real estate activities (unlikely) • Food and beverages, agriculture and fishing (likely) • Forestry, timber products, paper and containers and packaging (likely) • Healthcare and pharmaceuticals (likely) • Information technology and telecommunication (likely) • Media, publishing, arts and entertainment (unlikely) • Mining, metals, chemicals and resources (including oil and gas) (possible) • Professional and administrative services and supplies, including legal, consulting and accounting services (unlikely) • Public sector (unlikely) • Transportation, logistics, and storage (unlikely) • Utilities: gas, water and electricity (unlikely) • Waste management and recycling (unlikely) • Other (N/A) (d) Once you have chosen your search criteria you will be presented with a list of companies. For example, searching for “Fashion, textiles, apparel and luxury goods” over £500 million turnover in 2021 provides a list of 93 companies, including some of the largest UK based retailers such as H&M, Burberry, Calvin Klein, Hilfiger, and many leading supermarkets: (e) From your search results list, select 10 companies to focus your analysis on (NB. you should include a list of the companies that you have focused on and your rationale for selecting them as an appendix to your report (not included in the word count – see Appendix 2)). (f) Using the links on the database, (i) connect to the Modern Slavery statements for each of the selected companies and read and review the reports, and (ii) review the ‘statement summary’ which provides a high-level summary of the company’s reporting that year. An example for H&M is provided below: (g) Assess the reports against the key criteria identified below and as discussed in class (from Hsin 2019 and Voss et al 2019): (i) Compliance with reporting requirements: is the statement visible on the company’s customer facing website; has it been signed off by an executive board member? (ii) Does the statement cover the company’s policies towards modern slavery? (iii) Is there transparency around the company’s structure and its value chain and reach (i.e. multiple tiers of the value chains)? If so, is this presented effectively to allow an assessment of risk with regard to Modern Slavery? (iv) Does the statement discuss how the company audits their activity in the value chain? Who undertakes the audits (are these independently undertaken)?Is there mention of scope for worker involvement in the auditing process? Is there discussion of auditing beyond first tier suppliers? (v) Does the statement discuss the due diligence processes it undertakes with respect to modern slavery? Is there discussion of due diligence beyond first tier suppliers? (vi) Does the statement discuss how the company undertakes a risk assessment regarding modern slavery across its supply chains? Is there discussion of assessment of risk beyond first tier suppliers? (vii) Do employees and contractors receive training on identifying and dealing with modern slavery in the value chain? Is it clear who in the company receives this training? Is training provided to others throughout the value chain? (viii) Is there any discussion about steps to remediate the consequences of modern slavery if it is identified in the company’s value chain? Are these likely to be effective? (h) Use your analysis to produce a report which summarises your findings for the sample of companies you have chosen. The structure for the report is provided in Appendix 2 with details of the mark scheme and how your report will be assessed. You may choose to present findings in tables or other graphical forms, but please also provide a summary textual analysis of key points. (i) Include a final section which reflects on your findings, especially with regard to your assessment of the effectiveness of the UK’s approach to modern slavery reporting requirements and what businesses might do to improve social sustainability. In this reflection, please draw upon the assessment of strengths and weaknesses of the approach discussed in the literature (see refence list below and in class materials). (j) A detailed mark scheme for the coursework report is provided in Appendix 2. 4. Submission details Submission deadline: Thursday 2nd May 2024, 16:00 Word length: 1,200 words Submission process: you should submit your report in Word or as a pdf on Canvas Turnitin on the module Canvas site.
ECON GU 4251: Quiz 1 Spring 2024 Answer this to the best of your ability, we do not keep track of your identity. This is to test your understanding of the class material and to provide feedback to the instructor and TA on strength and weaknesses of the class as the semester progresses. Feel free to collaborate with your peers, but beware that you may want to ensure that you would be able to answer to these questions independently. Average cost, marginal cost, and minimum efficient scale A firm has total cost function TC(q) = 0.5q2 + F, where F > 0. a. Derive the firm average cost curve, marginal cost curve, and minimum efficient scale. b. If the price isp = 10, and the firm is perfectly competitive, what is the highest fixed cost F at which this firm will produce a positive quantity? When this is the case, how much will the firm produce? Willingness-to-pay for quality There are three consumers i = 1, 2, 3, each being characterized by a value of θi: θ1 = 1; θ2 = 2; θ3 = 3. A good has quality δ(> 0), and the utility for individual i when purchasing the good at price p is the familiar form. The marginal cost for the firm producing the good is constant, but also a function of quality: MC(q) = 1.5δ2 . a. Compute price, quantity, and consumer surplus when δ = 1. b. How would quantity and consumer surplus differ if δ = 2? c. What about if δ = 0.5?
ENGL 1007 Task 2: Interview Plan Context: To develop your Humans of New York-style. series, you will be collecting interviews from three people and transcribing them. You are transcribing the interviews to better curate a textual narrative from them. You can find more details about how to record and transcribe your interviews in this information sheet. Recall these two videos from Brandon Stanton on how he approaches interviewing for Humans of New York. 1. Mashable, "This is the Human behind HONY" (3:11) 2. TEDx Columbia College, "Brandon Stanton: The Good Story" (16:20) Task (250-350 words): 1. Give a brief explanation of the topic you chose and why you chose it. a. What are you hoping to learn about this topic through your interviews? 2. List the three people you are interviewing. a. Then, give a brief explanation of why you have chosen the people you have. What perspective(s) do you think these people will have about your topic? This is not a binding statement should your plans change over the next week or so. 3. You will formulate three to four interview questions total that emerge from the patterns (keywords and categories) you began to see in yours and/or your classmates’ narratives. a. These interview questions should help you learn more about people’s educational experiences based on what interests you from your peers’ narratives. You will use Brandon Stanton’s approach and ask your interviewees “Tell me about a time when…?” as your first question. b. Then, develop two to three follow up questions designed to allow respondents to discuss their impressions or experiences in some detail. Remember that your interviews should be between five and ten minutes long; avoid asking questions that solicit only yes or no responses. 4. You will also need each person's consent to interview and photograph them. a. We will follow “human subject research protocols,” which form. an ethical code for treating people with respect, consideration, and empathy when conducting research. Human Subject Research protocols are rooted in the maxim “do no harm.” Thus, a statement of consent needs to be recorded at the beginning of the interview. b. You can interview people in their home language, but the transcript. will need to be translated into English. c. In addition to your three interview questions, draft a statement of consent statement that you will ask your interviewees to read at the interview's beginning. i. For example: “Do you consent to this interview and your photo being shared with my instructor and class for the purposes on an English assignment?”
ASB-3525 – BANK MANAGEMENT ASSIGNMENT (SEMESTER 2, 2023/24) (20% of total module mark) SUBMISSION DEADLINE – 23:59 15TH APRIL 2024 Please submit an electronic copy ONLY via Turnitin You are reminded not to copy material from any sources without properly referencing it, as this constitutes plagiarism: cases of plagiarism will be referred to the Business School Academic Integrity Officer and will be subject to a deduction of marks, which can result in an overall mark of 0%. Background You have to apply the skills you have learnt during Lecture 1, Lecture 2, Lecture 3 and Lecture 4 to answer the assignment question. You must answer all your questions (part1, part2 and part3) in one document (i.e. Word) and you can provide screenshots or copy and paste your working from Excel into the document to support your answer. Your answers need to be clear and concise. The total word limit for the report is 1,000 words. All data required to complete the assignment is provided below. Assignment PART 1 (worth 20% of the total assignment marks) A senior bank manager has asked you to analyse the profitability of selected customer relationships. The procedure is to estimate the total expense associated with account activity and compare this with projected revenues. Data from Table 1 can be used to answer the questions in Part A and Part B. A. The typical low-balance customer at your bank with an average monthly demand deposit balance under £175 exhibits the following monthly activity: 30 withdrawals (8 electronic), two transit checks deposited, one transit check cashed, two deposits (one electronic), and one on-us check cashed per month. Assume there is one account maintenance for an account in which checks are not returned and that net indirect expenses apply. Use the unit cost data to estimate the average monthly expense for the bank to service this account. Suppose the bank can earn an average 5.8 per cent annually on investable deposits (ledger balances minus float minus required reserves). The typical customer keeps an average monthly balance net of float equal to £112 in the account and pays a £3.23 monthly service charge. The bank must hold 10 per cent required reserves against the average balance and thus can invest 90 per cent of the balance. Determine whether the account is profitable for the bank. B. The typical interest-checking account customer at your bank maintains a monthly balance of £1,150 net of float, writes 34 checks or withdrawals (21 electronic), deposits four transit checks, cashes two transit checks, makes two deposits (one electronic), and cashes one on-us check per month. Assume there is one account maintenance for an account in which checks are not returned and that net indirect expenses apply. Interest is paid on the account at an annual 1.5 percent rate. Use the unit cost information to determine whether this account is profitable. Assume the bank collects no service charges and can again earn 4.5 percent on investable balances net of 10 percent required reserves. PART 2 (worth 30% of the total assignment marks) The senior bank manager has also asked you to calculate forecasted weighted marginal cost of funds Table 2 provides information that can be used to estimate Bangor Local Bank’s weighted marginal cost of funds. The estimates represent a best-guess forecast of the funding sources and associated costs for the year. Calculate the bank’s forecasted weighted marginal cost of funds. Discuss how a bank’s core deposits differ from its wholesale liabilities in terms of interest elasticity. What factors are relatively more important for attracting and retaining core deposits as compared with purchased funds? PART 3 (worth 50% of the total assignment marks) Explain the objectives of a bank’s contingency funding plan and describe what it includes.
Project #1 – Fill-in Code Given the starting file, fill in all the blanks with your own code Your Task Your task is to finish the given python file with lines of code that solve the problem described. Part of this assignment is to test how closely and precisely you can follow the directions below. There are 10 TODOs laid out in comments in the program. Additionally, there are three extra credit assignments at the end of the program. All of the problems can be solved with writing only a single line, but you may write multiple lines if you prefer. You do not have to add any other code to the file than what is laid out in the file. You may want to add extra print statements to help find errors in your program, but these are not required and should be removed/commented out prior to submitting the project. You are not allowed to omit any code we ask you to complete. Omitting an answer will result in a loss of points. You will be penalized if the statements in the program do not work in the same general way as the problem describes, even if the program works correctly otherwise. After the project is due, your program will also be graded by hand. The autograder is not necessarily the final grade you will receive on the project. You must include a comment at the top of your program containing your name, “Project #1”, and the date you turn it in. (Or you will lose points) Link to project file: https://drive.google.com/drive/folders/1drx6pV1kyO30Y-htha47IHqD73_RIfpL?usp=sharing Save your program as Project1.py. This needs to be the name of your file for the autograder to run correctly. If you are failing every test, check the details to see if your file was named exactly correctly. Testing Test your program completely. Run it several times: verify that for each section outputs the desired values, and that the prints match exactly to the desired. Once you have confirmed to yourself your program is functioning, you should submit it to the appropriate place on gradescope.com. If you fail any tests, gradescope will tell you which test, a small amount about the test, but it is up to you to figure out what went wrong. This is a very important part of the programming process. Extra Credit There are three places indicated in the code where extra credit can be gained. You may do any, all, or none of these. You will not be penalized, but you won’t get any extra credit, if you attempt an extra credit and it doesn’t work correctly. Extra Credit #1 In order to complete extra credit 2 and 3, we need to use the premade math functions that come with python. This TODO should be a single line that allows us to use the functions from the math library. Extra Credit #2 Fill in the mathematical equation so that the line " fac_by_hand = 1 " calculates the value of 5! [5 Factorial] and stores it into a variable called fac_by_hand. This calculation should only use the standard python multiplication (*). Then do the same with the second line " math_fac = 1 ", so that the 5 factorial is calculated using the math library's factorial function. The print out for this TODO should read 120 is equal to 120. Remove the comment symbol from the line: #print("TODO 12 Attempted") in the starter code so the autograder can tell you attempted it. Extra Credit #3 Pick a function from the math module, use it correctly and print out the result (a list can be found here: www.w3schools.com/python/module_math.asp). Remove the comment symbol from the line: #print("TODO 13 Attempted") in the starter code so the autograder can tell you attempted it. Submission When you are done, turn in the assignment via Gradescope, you should submit only your .py file. Make sure that it is named Project1.py. MAKE SURE YOUR NAME IS IN IT OR YOU WILL LOSE 10 POINTS (See rubric below) After you submit, gradescope will automatically test your program, and you should shortly see the results from the tests. If you have failed any, a small amount of feedback might be given, and you will be allowed to resubmit your code. It is up to you to figure out what went wrong. This is a very important part of the programming process. We may offer assistance in finding the bug, but we will not bug fix for you. After the project is due, your program will also be graded by hand. The autograder is not necessarily the final grade you will receive on the project. Here is a little step-by-step video I made explaining one way to upload you .py file to gradescope: https://youtu.be/XTnnhdwdloY Grading After the due date, your project will also be hand graded. We are looking to see if your project was completed authentically, and if there are parts of your code that are partially correct and deserve partial credit. In the report of your grade, you will see a score and a set of letter codes explaining what you did wrong. If you get 10 points, there will be no associated letter codes. The grading codes A-E are defined and will be the same for all programs that you turn in. A summary of those codes is as follows: A: -10 Student’s name is missing from the top of the program. B: -100 Program cannot run due to syntax errors. C: -100 Program crashes before finishing. D: -10 (once) Program uses overly advanced methods not yet discussed in class E: -25 (once) Program works correctly, but changes the assignment in order to do it. In addition, penalties for this assignment only will be incurred for the following infractions (which may supersede some of the generic codes listed above): F: -10 (each) Program is missing a solution to a required problem. G: -10 (each) Required line of code is omitted (like omitting a Print statement, for example, either in part or in its entirety). H: -25 (once) Project file is not named correctly, causing autograder to fail. Each of the three extra credit items are worth +3.33 points added to the score only if implemented correctly. Incorrect implementation will not be penalized.
MATH2003J, OPTIMIZATION IN ECONOMICS, BDIC 2023/2024, SPRING Problem Sheet 5 Question 1: Consider the following LP problem: Maximize z = 7x1 + 4x2 subject to 2x1 + x2 ≤ 20, x1 + x2 ≤ 18, x1, x2 ≥ 0. (I) Solve the above problem using the graphical method. (II) Solve the above problem using the simplex method. Question 2: Consider the following LP problem: Maximize x1 + 2x2 subject to x1 ≤ 2, x2 ≤ 2, x1 + x2 ≤ 3, x1, x2 ≥ 0. (I) Solve the above problem using the graphical method. (II) Solve the above problem using the simplex method. Question 3: Consider the following LP problem: Maximize z = 9x1 + 8x2 subject to x1 + x2 ≤ 6 2x1 + x2 ≤ 8 3x1 + 2x2 ≤ 13 x1, x2 ≥ 0. (I) Solve the above problem using the simplex method. (II) Solve the above problem using the graphical method. Question 4: Use the simplex method to solve the following LP problem: Maximize 5x1 + 4x2 subject to −3x1 − 5x2 ≥ −78, 4x1 + x2 ≤ 36, x1, x2 ≥ 0. Question 5: Use the simplex method to solve the following LP problem: Maximize 4x1 + 2x2 subject to x1 + x2 ≤ 50, 6x1 ≤ 240, x1 ≥ 0. Question 6: Use the simplex method to solve the following LP problem: Maximize P = 3x + y + 4z subject to 3x + 5y + 10z ≤ 120, 5x + 5y + 2z ≤ 6, −8x − 3y − 10z ≥ −105, x, y, z ≥ 0. Question 7: Use the simplex method to solve the following LP problem: Maximize 5x1 + 6x2 + 4x3 subject to x1 + 2x2 + x3 ≤ 180, 3x1 + x2 + 2x3 ≤ 300, x1 + 2x2 + 2x3 ≤ 240, x1, x2, x3 ≥ 0. Question 8: Use the simplex method to solve the following LP problem: Maximize z = 4x1 + 5x2 + 3x3 subject to 3x1 + 2x2 + x3 ≤ 5, 4x1 + 3x2 + 2x3 ≤ 8, x1 + 4x2 + 2x3 ≤ 11, x1, x2, x3 ≥ 0. Question 9: Use the simplex method to solve the following LP problem: Maximize z = 5x1 + 4x2 − 6x3 subject to 4x1 + x2 − x3 ≤ 19, 3x1 + 4x2 − 6x3 ≤ 30, 2x1 + 4x2 − x3 ≤ 25, x1 + x2 − 2x3 ≤ 15, x1, x2 ≥ 0, x3 ≤ 0.
Project #2 – Big Practice Making many files to solve many different problems Your Task Your task is to solve all the provided problems using the python skills we've learned so far. There are 6 problems to solve. Each one should be done in their own .py file, and they must be named exactly what is asked for. Note the points for each problem All problems should be no more than a couple of lines. Occasionally you will be asked to include certain lines at the start of the file. You will be penalized if the statements in the program do not work in the same general way as the problem describes, even if the program works correctly otherwise. After the project is due, your program will also be graded by hand. The autograder is not necessarily the final grade you will receive on the project. You must include a comment at the top of all your program files containing your name, “Project #2”, and the date you turn it in. Problems 1. A starting example repeat.py (20 point) The first program is provided to you as a starting example. It’s already implemented. All you need to do is to download the file, open it in VSCode, add your name/date. You do NOT need to change the program code. This example reads in a user input, stores it in a variable, and prints it back to the terminal. After you have edited the comments, save it. You can then run it, try some different inputs, and verify the outputs are correct. File download: repeat.py (click download button at the top by the printer icon) This first problem should now serve as your template for the rest of the problems 2. Implement temp.py (20 points) Create a new program, name it temp.py This program will first ask the user to enter a floating point number representing a temperature in Fahrenheit. It should then convert the input number to Celsius and Kelvin respectively, and print them out on separate lines. The formulas for temperature conversions are: C = (F - 32) * 5 / 9 K = C + 273.15 Where F is Fahrenheit, C is Celsius and K is Kelvin. Running a correct implementation of this program could look like: Enter temperature in Fahrenheit: 31.41 31.41 degrees Fahrenheit is equivalent to: -0.3277777777777777 degrees Celsius 272.8222222222222 Kelvin Formatting details: ● The last number on the second-to-last line must be the Celsius value ● The last number on the last line must be the Kelvin value ● No other lines of text or additional formatting is necessary. Do NOT print extra lines. Do not worry about the number of decimal places, just include all you get from the conversion process (ie don't round or cast the result) 3. Implement cube.py (20 points) Create a new program, name it cube.py This program will first ask the user to enter an integer representing the side length of a cube. It should then compute the volume and surface area of the cube, and print them out on separate lines. For a given side length: The volume is the side length cubed The surface area is 6 times the side length squared (as a cube has 6 sides) Running a correct implementation of this program could look like: Enter the length of the cube: 5 A cube with length 5 has: Volume of 125 Surface area of 150 Formatting details: ● The last number on the second-to-last line must be the volume as an integer number. ● The last number on the last line must be the surface area as an integer number. ● No other lines of text or additional formatting is necessary 4. Implement add_or_find.py (15 points) Download this file: add_or_find.py After the creation of the list names on line 2, your program should: ● Ask the user what they want to add to the list ● If the item is already in the list, print the index where it is found ● If the item isn't in the list, add it to the end, and print out the list. Running a correct implementation of this program could look like: Add a name? whalers ['blues', 'canucks', 'ducks', 'jets', 'kings', 'kraken', 'panthers', 'penguins', 'rangers', 'wild','bulls', 'cavaliers', 'celtics', 'kings', 'knicks', 'lakers', 'raptors', 'rockets', 'suns', 'warriors', 'whalers'] Add a name? ducks Already in the list, index: 2 The prints described above must be the last thing your program prints out before it ends. Do not print anything else after it or it will fail the autograder. HINTS: ● To test if a value is in a list, you can use the membership operator (in) (link) ● To find the index of a value you know to be in a list, you can use the index() method (link) ● I made this one sports themed, for all you sports-heads 5. Implement triangle_id.py (10 points) Create a new program, name it triangle_id.py This program will first ask the user to enter three different integers. We will call them a, b and c. Each represents the length of a side of a triangle (a and b are the legs, c is the hypotenuse). Your program should print out invalid, equilateral, isosceles, or scalene depending on the values of a,b,c. A triangle is invalid if the length a+b is less than or equal to the length of c. A triangle is equilateral if a, b, and c are all the same length. A triangle is isosceles if two of a, b, and c are equal (for example if a=b but != c). If a triangle isn't any of the previous types, we will say it's scalene. YOU DO NOT NEED TO UNDERSTAND THE UNDERLYING MATH TO SOLVE THIS PROBLEM. You just need to know how to take the above rules and turn them into code. This is a simple control flow diagram describing the solution to the problem. Use the tools we talk about in class to convert this diagram into code. Remember triangles represent branches, the code should start at start, and only be able to follow along the arrows.: Running a correct implementation of this program could look like: Enter a: 5 Enter b: 5 Enter c: 5 equilateral Enter a: 5 Enter b: 5 Enter c: 9 isosceles Enter a: 5 Enter b: 5 Enter c: 12 invalid The type of triangle must be in the last line your program prints out. HINTS: ● To find if a triangle is equilateral, you need to do three different Boolean expressions. Those Boolean expressions need to be combined in some way, it will be worth your time to review the reading on logical operations (also this link: here) ● To find if a triangle is isosceles, you need to do three different Boolean expressions. The expressions themselves will look like your solution to finding equilateral triangles, but you will combine them differently. Review the same materials as above, but pick a different way to combine them. 6. Implement even_division.py (10 points) Create a new program, name it even_division.py Division is made up of two parts, the dividend and the divisor. The number that is being divided is the dividend, the number which we divide by is the divisor. This program will first ask the user to enter the dividend, and then ask them to enter the divisor. Both will be integers and the user will never enter anything invalid (like giving 0 as the divisor). The program should then check to see if the dividend is divisible by the divisor. A number is divisible by another if the division results in no decimal values. For instance, 12 is divisible by 3 (the result is 4) but it is not divisible by 5 (the result is 2.4) *The program should output "True, {dividend} is divisible by {divisor}" or "False, {dividend} is not divisible by {divisor}" depending on the circumstance. Note, the print out should put the numbers in place of {dividend} and {divisor}. So for 12 and 3 this should be printed out "True, 12 is divisible by 3" Running a correct implementation of this program could look like: Enter dividend: 12 Enter divisor: 5 False, 12 is not divisible by 5 The formatting of this line needs to match the described* exactly, and it needs to be the last thing your program prints out 7. Implement anagram.py (5 points) Create a program, name it anagram.py A string is said to be an anagram of another string if it can be created by rearranging the letters of the other string. For example, fried is an anagram of fired and vice versa. Another example is listen and silent. Your program should accept two strings, and should print out True if they are anagrams. It should print out False otherwise. YOU CANNOT USE LOOPS TO SOLVE THIS PROBLEM. Running a correct implementation of this program could look like: Enter first: santa Enter second: stana True HINTS: ● You do not need loops, or branching to solve this problem. In fact, using them could make the problem much harder than it would be otherwise. ● Strings are hard to use, is there a way to turn them into a list of characters? ● Lists have many built-in methods that could be useful. What do all anagrams have in common? Could you reorder both lists to make identifying anagrams easier? ● Often solving CS problems is like solving a problem. You have to think about anagrams in a new way in order to teach them to a computer. ● BTW lists have a built in sort method, I wonder how that could be useful here???(https://www.w3schools.com/python/ref_list_sort.asp) Testing Test your programs completely. Run it several times: verify that for each section outputs the desired values, and that the prints match exactly to the desired. Once you have confirmed to yourself your program is functioning, you should submit it to the appropriate place on gradescope.com. If you fail any tests, gradescope will tell you which test, a small amount about the test, but it is up to you to figure out what went wrong. This is a very important part of the programming process. Extra Credit The extra credit are three additional problems you can attempt. These problems are meant to really test your understanding up to this point. Extra Credit #1 Create a new program, name it perfect_weave.py This program requests 3 inputs in order: ● A string, referred to as A here ● Another string, referred to as B here ● An integer, referred to as n here It will then print out n copies of A with n copies of B interweaved / interleaved. So the output should look like ABABAB… in other words: A followed by B, repeated n times. Running a correct implementation of this program could look like: Enter first string: on Enter second string: i Enter a number: 2 onioni Enter first string: flip Enter second string: flop Enter a number: 4 flipflopflipflopflipflopflipflop Hints: Try to do a few examples by hand first, looking for a pattern in how the output relates to the input. The solution to this problem is deceptively simple, remember that we have already learned about an operator that lets us repeat strings! Extra Credit #2 Create a new program, name it fraction_division.py Division is made up of two parts, the dividend and the divisor. The number that is being divided is the dividend, the number which we divide by is the divisor. The goal of this program is to show integer division results with fractions. The user inputs the dividend first, and then the divisor. You can assume both are positive integers. Your program should then print out a string showing the integer result of the division, including the quotient and remainder. Follow examples below for more insight. Hint: the arithmetic operations you need to solve this problem already exist in Python. This is also meant to test your knowledge of strings to get a perfect recreation of the formatting shown below. Note that after the equals: there is a newline and a tab. Note: unlike the previous questions, for this question the formatting must exactly match the examples given below. What is the dividend: 7 What is the divisor: 2 7/2 equals: 3 and 1/2 What is the dividend: 50 What is the divisor: 10 50/10 equals: 5 and 0/10 What is the dividend: 147 What is the divisor: 6 147/6 equals: 24 and 3/6 Extra Credit #3 Create a new program, name it seconds.py, and implement it to complete the following task: 1. ask the user to enter a positive integer representing the number of seconds. 2. convert that to a total number of days, hours, minutes, and seconds such that hours must be between 0 and 23, minutes between 0 and 59, and seconds between 0 and 59. For example: 3599 seconds converts to 0 days, 0 hours, 59 minutes and 59 seconds; 90061 seconds converts to 1 day, 1 hour, 1 minute, and 1 second. 3. output the result in 5 lines: the first line is the original number the user entered, followed by a space character, and the text seconds is equal to: then lines 2 to 5 are the number of days, hours, minutes, and seconds that you calculated. Hint: for this program you will need to use the floor division operator // and the modulo % operator. First think about how to solve this problem by hand; next, write down code to implement your solution. Then test your program by running it with a few example inputs like those listed above. Running a correct implementation of this program may look like: Enter a number of seconds: 314159 314159 seconds is equal to: 3 days, 15 hours, 15 minutes, and 59 seconds. Submission When you are done, turn in the assignment via Gradescope, you should submit only your .py file. Make sure that your file names match exactly. After you submit, gradescope will automatically test your program, and you should shortly see the results from the tests. If you have failed any, a small amount of feedback might be given, and you will be allowed to resubmit your code. It is up to you to figure out what went wrong. This is a very important part of the programming process. We may offer assistance in finding the bug, but we will not bug fix for you. After the project is due, your program will also be graded by hand. The autograder is not necessarily the final grade you will receive on the project. Grading After the due date, your project will also be hand graded. We are looking to see if your project was completed authentically, and if there are parts of your code that are partially correct and deserve partial credit. In the report of your grade, you will see a score and a set of letter codes explaining what you did wrong. If you get 10 points, there will be no associated letter codes. The grading codes A-E are defined and will be the same for all programs that you turn in. A summary of those codes is as follows: A: -10 (once) Student’s name is missing from the top of the program. B: -100 a Program cannot run due to syntax errors. C: -100 a Program crashes before finishing. D: -10 (once) Program uses overly advanced methods not yet discussed in class E: -25 (once) Program works correctly, but changes the assignment in order to do it. In addition, penalties for this assignment only will be incurred for the following infractions (which may supersede some of the generic codes listed above): F: -10 (each) Required line of code is omitted (like omitting a Print statement, for example, either in part or in its entirety). G: -15 (once) Project file is not named correctly, causing autograder to fail. Each of the three extra credit items are worth +3.33 points added to the score only if implemented correctly. Incorrect implementation will not be penalized.
BML 302 Developing an Information Strategy Reassessment Project Should you fail to achieve the pass mark and be required to undertake a reassessment in accordance with University regulations, you will need to undertake the following: Re-assessment task (3500 words) You will need to re-submit Part 2 of the assignment based on the case study provided in the handbook and taking account of the comments provided in your feedback where work was submitted and also of the increased word count. This will require that you address certain issues in more detail. The second part of the assessment is the preparation of the IS strategy in report format for the case study business introduced in Part 1 of the assessment. Following a brief summary of the objectives for the strategy identified in Part 1 and adjusted to take account of any feedback provided, the strategy will need to discuss the applications, technologies and organisational changes required to meet the changing business needs. An overview of the implementation plans and change management implications will also need to be presented. It should be noted that you do not need to start from the work you submitted in Part 1 and you can completely revise your original analysis. Your strategy should demonstrate: § Coherent and critical presentation (using appropriate analysis tools to support the argument) of the proposed IS following a logical argument and covering applications, infrastructure and organisation § Critical discussion of the necessary governance, plans and change management issues associated with the implementation of the IS § Discuss the business benefits of adopting the IS and the alignment with business strategy § The report should be presented in a clear and logical manner, being appropriately structured and supported using high-quality referencing. Specific assessment criteria are as follows: Assessment Criteria Weighting (%) Short summary of the business objectives that have a direct influence on the IT strategy as defined from Part 1. Summary of the SWOT related to the existing IT infrastructure and organisation. Presentation and discussion of the Goals and Objectives for the IT Strategy. 20 Comprehensive discussion of the proposed information strategy demonstrating how it aligns with business objectives, delivers benefits and how it will support future business sustainability. Detailing the prioritised Critical Success Factors and essential criteria to be met, it should cover as a minimum: · Applications required · IT Infrastructure and architecture solution · IS organisation, management and processes References should be used in support of your strategy. For example covering, systems proposals, architectural approaches, IT support services, security and staff structures. 45 Critical and referenced discussion of the change management issues to be addressed and key activities needed to implement the strategy; · Outline project phasing/timeline · Programme management · Risks and risk avoidance measures · Budget and benefits 20 Generate a high quality report: · Clear structure in which the strategy is coherent and understandable from a business management perspective (i.e. not a disconnected set of results from analytical tools). · The account should be presented effectively using ICT and be well structured (following a pattern similar to the structure discussed in tutorials) and coherent. It should include title page, contents page, numbered headings and subheadings. · There should be evidence of research conducted using a variety of sources (books, internet, journals etc). · All articles should be correctly referenced using Harvard and a bibliography should be included before the appendices. · Good use of standard English should be evident. 15
GSOE9510 - Summer 2025 The Fishery Challenge (Team Project) Summary This project focuses on the learning objective of sustainability, but involves consideration of ethics, context and teamwork, too. You will work in a team of 10-12 students. Note that the groups formed for this game are independent of your workshop groups or sessions. Students from different workshop groups and sessions can also form a group together to play the fishing game against other teams. PART 1 involves you playing a simulation game as part of a team. You will be playing against the other student teams. (Study the marking scheme (attached) and you will see that the winning team gets an extra mark!) The game is described below. It involves you accumulating ‘wealth ’ by ‘fishing’ from a common stock of fish. For PART 2 you will write an individual short summary about what you have learnt from this whole project and describe how your team operated. The requirements for this report will be given once the game is over, as they will depend, in part, on what happens during the game. Team membership: You must select your project team on Moodle. Course Syllabus Materials> Select A Project Team Marks: You are reminded that this project will count as 15 % of your summative mark in this course and is a team mark. Additionally, you will reflect on your experience playing this game and creating the learning resource. This will count as 10 % of your summative mark in this course and is an individual mark. Learning Objectives With reference to the GSOE9510 learning objectives, this activity will help you learn about the following. Organisations & leadership Specifically, by considering the team in which you work Engineering’s context There are many perspectives on a technology, besides the purely technical one. Sustainability This is the major focus Identifying problems of ethics Noting that the profession has nominated sustainability as an ‘ethical good’. Over the next few weeks, we will build further on these ideas. You will be involved in many discussions with the rest of the class. In these discussions, the diversity of perspectives is important. In your professional practice, too, you will need to communicate with many parties who do not share your engineering view of a problem. You are well aware of how failure to consider the context of an engineering design often leads to a serious failure of the overall system. You will also need to examine messy problems, i.e. those with uncertainties and multiple conflicting aims, from several different perspectives. Background Sustainability does not have a simple explanation. In essence, it is about the future, specifically whether a system can persist into the future and, if so, in what form. Analysis of, and subsequent decisions about, sustainability often follows a computer-based simulation of a scenario playing out as away to predict the future. This project is based on such a simulation, examining a ‘fishing system. ’ It will involve ecological, economic and technological aspects, but not social. Note, too, that a simulation should match reality. Reality includes ambiguities and random events. Malthus is famous for arguing that indefinite linear growth models are nonsensical in reality, but it was Verhulst who introduced the logistic equation to give mathematical form. to this observation. Lotka and Volterra independently studied the interaction of predators and prey by using nonlinearly coupled equations. The latter applied his work to a successful study of Mediterranean fisheries. Such coupling between different components (equations) in a system (model) means that the system maybe chaotic, depending on the precise values of the model’s parameters. Such a situation is not unusual in engineering. For example, the equations governing lasers show similar potential for such behavior. More generally, chaos is a consequence of systems having some form. of feedback, which is a surprisingly ‘normal’ circumstance. However, the identification of domains of chaos is usually a very difficult mathematical challenge. Chaos is a mathematical state; it means that we cannot have a deterministic knowledge of the future. Alas, this ‘inconvenient’ possibility is often neglected by those who use models. Remember, too, that any modelling is only as good as the assumptions being made, some of which depend on intrinsically imperfect measurements of reality. PART 1 – ‘Playing the Game’ Your team is one of N competing in a game. Each round (Round n) of the game you must complete instructions and submit them to Baruwaluuwu using the designated discussion tool on Moodle. The outcome of that round of play will be posted on Moodle soon thereafter. Your team’s instructions for each round are due according to the times in Table 2 below. You see we plan to play 12 rounds in total. The first set of instructions is due 6 pm Tue 11 January. Goal You will win the game if you have the highest value of assets at the end of play, assets being the total of your bank balance and there-sale value of your fishing units. Your team’s sources of wealth are fishing and bank interest which earnt by your monetary reserves. Fishing units Of course, catching fish is an ‘unnatural’ action for humans (unlike, say, pelicans or dolphins). To catch fish, you need to use ‘technology’ meaning, in this case, a fleet of fishing units. These can be bought (and sold) during the game. Each round, your team gets paid for its fishing catch at the rate 10 CU/UoF, where UoF denotes Units of Fish and CU denotes Currency Units. As your team gains more wealth, it can provide engineers with the resources needed to introduce new technologies, i.e. better ways to catch fish. First, they can make units mobile. Second, they can make them more ‘efficient’ (measured by UoF/fishing unit). Mobile-fisher yes 1. A local-fisher can only fish in the fishing ground off the port where it was built. It cannot be relocated and it only fishes in the port which is assigned to the team. A mobile- or heavy-fisher can fish in any fishing ground. 2. Haul is the factor used to calculate the catch. A heavy-fisher catches 5 times as much in terms of UoF, all else being equal. 3. Fishing units have operating expenses each round. Each unit incurs a baseline cost of 50 CU/round. The additional expense depends on whether the unit is off-shore or in-shore. For example, a local-fisher working in-shore costs 100 CU/round; a heavy-fisher off-shore costs 400 CU/round. 4. A fishing unit can be scrapped (sold to recyclers). Scrap value is fixed, at 15 % of initial cost. Ship-building In any round, the engineers (ship-builders) can only accept total orders from all teams of 20% more than the total orders of the previous round. Engineers cannot expand their business at an infinite rate: new staff take time to train. Their activities will contract if no business is forthcoming: engineers will leave the industry. Obviously if there are no orders from anyone, the engineers go out of business! To prevent their business from being exposed to any particular team’s financial failure, the shipbuilders limit the size of your team’s order. In any round, no team’s order can exceed one-third the ship-builders’ total capacity. If total orders exceed the maximum ship-building capacity available, the excess will be deferred into the next round (or later). Each fishing unit is built at the same rate, which means cheaper units are finished first. You are charged half the price of the ordered unit in the round when you order it; you are charged the second half in the round when it is completed. This maybe the same round, so be prepared to pay full price immediately. You cannot use it for fishing and it costs no operating costs until the round after delivery, i.e. when you can use it. You may cancel an unfinished unit, but you do not get the deposit refunded. The fishing area The fisheries consist of in-shore and off-shore fishing grounds, forming concentric circles as shown in Fig 1. The FOUR interior, off-shore grounds are denoted W, X, Y & Z. The 2N exterior, in-shore grounds are denoted by A, ab, B, bc, C, cd, etc. Every second in-shore sector has a port. Fish stock surveys If you want to know something about the population of fish, then you must spend money on research. Whenever one of your fishing units works in a particular fishing ground, you can pay for a fish-stock survey which will tell you the population of fish during that round of play in that specific fishing ground. Each in-shore fishing survey costs 10 CU and each off-shore survey costs 20 CU (because you need to pay for more travel-time by the fish researcher). Financial considerations All transactions are rounded to the nearest CU. Your team’s financial balance is calculated at the end of each round. If the balance is positive, interest at rate +r is added to your account. If the balance is negative (i.e., you are in debt), interest at rate R is debited from your account. In this game, in an era of low interest rates, r = 0.05 and R = 0.08. A team’s maximum permissible debt (or overdraft) D is at least 450 CU. It increases when the fishing business is operating successfully, and at the end of Round n, it is calculated from the income from fishing in Round (n − 1). D = R/value of catch − operating expenses CU If its debt exceeds this permitted maximum, there must be a sale of your team’s assets, i.e. fishing units, at the start of the next round to get it within the limit. If a team’s balance cannot get within its permitted overdraft, then it is BANKRUPT. Bankruptcy Bankruptcy is part of the ‘business cycle.’ If a team is bankrupt, then it misses the next two rounds of play (and doesn’t score the mark for avoiding bankruptcy). After sitting out these rounds, the team resumes play with 100 CU. Upon resumption, the team’s first decision is whether or not to order a new fishing unit. ‘In the beginning’ The game has the following initial conditions. • Your team has 1 local-fisher (unit xL01, with x ∈ {A,B,...} denoting your team) with a designated ‘home’ port, that differs for each team. (Recall that, when not in port, this fishing unit can only fish in this same space all game.) • Your team has 300 CU. • Your team’s permissible debt at the end of Round 1 is 450 CU. • The engineers can accept a total order from all teams for new fishing units of 225N CU in Round 1. Apart from the geography of Fig 1, there is no other initial knowledge of the fishing grounds. One round of gameplay For each round, the information you need to provide is shown in the examples of Figure 2. 1. Your team allocates each of its fishing units. Each unit should be either kept in port or sent to a specific fishing ground as shown on the map in Fig 1. Remember a local-fisher can only be sent to the fishing ground off the port where it was built, i.e. where it starts. Note that any unallocated unit will be assumed to be in port for the round. This incurs its baseline expense but catches no UoF. 2. Your team may buy and/or sell fishing units. Complete any forced sale needed to reduce your debt. Bought units can only fish in the round after they are delivered,i.e. you have finished paying for them. They are being built this round. Engineers work at a finite pace. Any deposit, though, is expenditure in the round a unit is ordered. You may scrap any unit in any round. Units sold will incur no operating costs in the round. After ‘playing’ each round,you get the current state of the game. The following public information will be available after each round. It will be posted in the public discussion by Baruwaluwu. An example is found in Figure 3. • total fishing units by type that were in each fishing ground • the total combined average catch of all fishing units for the round (Not yours, but for everyone combined.) • total capacity of the shipbuilder for the next round (You can order only up to 1/3 of that.) Each individual team will receive the following information from Baruwaluwu. Since you might want to keep this confidential, it will be provided in your team’s private discussion thread on moodle. Examples are found in Figure 4. • the individual catch and operating costs for each of its fishing units • the average stock of fish in any fishing ground for which a survey was bought • the detailed statement for its account • its currently permitted maximum overdraft and any need for a forced sale • the state of its orders with the shipbuilders NB: The numbers in the examples of Figs 2-4 may be impossible for the parameters (prices, interest rates, fish populations, etc) we use this year. Round 1 For Round 1, there are very few decisions to make. • Do you fish? or leave your local-fisher (unit xL01) in port? • Do you survey the fish population? • Do you order another fishing unit? Procedural matters Each team must decide instructions by the due date for each round. These must be submitted in the link:https://forms.office.com/r/0ziw5dv3ya. After the round is played, Baruwaluwu will reply with the outcomes for that round. Instructions for each round are due according to the table below, unless a subsequent message indicates that an extension is granted. Common information will be posted in the project’s common space in Moodle. The ‘missing’ times allow you extra time as a contingency for the preparation of the learning resource and also the in-class test. We plan to use the result of the game during the final tutorial activity in Week 5. This is a competitive game that exercises your communication skills and co-operation. It requires you to work with your team-mates. Study the marking scheme attached. You are not explicitly asked to exercise negotiation skills (though that probably will happen as it is intrinsic to working in any team). The following is the way that PART 1 of this project—‘playing the game’—will be marked (out of 8). yduedate for eachround minus0.5 per missing instruction4feedbackabout the game; el!Youareengineers;youcannothelpbutbecurious.Isations?4surpriseWill be revealed in the end ofthegame1TOTAL15
MENG 4019 - Practical 1 – 2022 Task: design and simulate the operation of a hydraulic curcuit. A hydraulic cylinder, stroke 2000 mm, D piston 60 mm, d rod 40 mm angled 60 degrees from horizontal is lifting a mass load of 4000 kg. The cylinder needs to be able to stop at intermediate positions. Firrst, we build a conceptual circuit: 1. Open Automation studio, select and insert the following components from the Hydraulic set of components 2. Click on Filter to select, Right click on Filter, click on Lock Size to unlock, reduce size of Filter (drag it to a smaller size), Right Click on Filter, click on Lock Size to lock 3. Connect circuit as shown below: 4. Select the Simulation tab and run a Normal Simulation. Then, Stop Simulation and run a Slow-Motion Simulation 5. This shows that the circuit is correct, and it works. The cylinder can extend, stop when needed, and retract. The components are all connected, there is no error reported by the system (To emulate an error, remove the connection between the filter and the tank. Try to run the circuit. An error will appear) Re-connect the filter and the tank. Check that all is correct and works. 6. Double click on the hydraulic cylinder. Open the Data tab. Ensure the star at the top of the Component Properties is unselected. Modify the characteristics of the cylinder as in the task definition and close the Component Properties: 7. Run the circuit. It is clear that the force exerted by the pressure (at approx. 80 bar – due to the relief valve) is insufficient to move the load. The reading on the flow meter is zero, the piston is stuck. 8. Click on the relief valve and increase the cracking pressure CP to 120, 121, 122 bar. See the influence of increased pressure. The piston starts moving. To have a smooth and fast motion, set the pressure at 150 bar. 9. Decrease the pump’s displacement to 40 cm 3 /rev. Examine the flow in the circuit. 10. Insert Node Dynamic, Differential Dynamic and Component Dynamic Measuring Instruments in strategic places to examine the operation of the circuit 11. Examine the dynamics of the operation of the circuit. Of particular importance are the pressure drops through different components. The whole circuit can be modelled as a series of resistances. 12. Click on the Y(t) plotter in the Simulation tab. Click on and drag the cylinder on the plotter. Select Linear Position, Linear Speed, Piston Side Pressure and Rod Side Pressure 13. Run the simulation in Slow Motion. You can see the wild and realistic variation of pressures and positions (due to oil and oil lines elasticity, inertia and friction). You can insert cursors, zoom in and out on x and y, display legend, select one or a couple of signals only, copy the plot and export the values for supplementary analyses. 14. Open Simulation Options in the Simulation Tab and in the Fluid Simulation pane, select perfect Lines. 15. Re-run the simulation. The spikes in pressure are a bit smaller, due to the elasticity of the hydraulic lines being removed as variable. 16. We want to be able to reduce the speed to about 150 mm/s (150 ±5 mm/s). This means we need to insert a variable throttle valve in the circuit (a variable hydraulic resistance). 17. Run the circuit in slow motion and modify the throttle valve opening (internal diameter) to set the speed as required. You can examine the speed value on the plotter or on the Component Dynamic Measuring Instrument Save the project.
BA (Hons) in Digital Marketing 5012MKT: Applied Advertising and Campaign Management (Part Time) Assessment Brief Due Dates: CW1: 3 Feb 2025 CW2: 24 Feb 2025 (Presentations will be held during tutorials) Coursework 1: Campaign Analysis (50%) – Individual Learning Outcomes Assessed by this Assignment 1. Explain the key stages of the communications planning process. 2. Define and evaluate appropriate measures for evaluating marketing communications activities. 3. Analyse an advertising campaign for a particular business scenario. 4. Explain how the creative idea and relationships are managed when using a range of marketing communications agencies and evaluate the selection criteria for choosing the agencies. Breakdown of CW 1 - Campaign Analysis: Section A: 1500 Words Section B: 500 words Summary This assignment allows you to revisit your analytical, academic, and critical engagement skills, as well as building your transferable skills such as research, time management/project planning and critically observing various aspects of an advertising campaign. You will learn the key requirements in campaign execution by reviewing an IMC campaign of your choice and unpacking key components to understand how it worked and identify areas for improvement. Assignment Description Tapping on key concepts and frameworks learnt in the module, with specific reference to Fill’s (2009) ‘Marketing Communications Planning Framework’, select a campaign for fashion brand that ran within the last five years. There are 2 components to this assignment. Review both tasks carefully before attempting the assignment. Section A: 1500 words Apply the following steps in Fill’s (2009) framework (in the following sequence) in your analysis. - Context Analysis (or Situational Analysis): Identify the current issues faced by the chosen fashion brand. - Marketing Communications Objective(s): What were the communication objectives for the chosen campaign? - Marketing Communications Strategy: What were the campaign strategies used? What was the core message of this campaign? How did the brand communicate this? Who was the target audience of the campaign? - Communications Tactics/Tools : What marketing communications tools were utilised in this campaign? Please include copies of advertisements, evidence of public relations efforts, or brand’s social media platforms, wherever applicable. - Scheduling : What were the (estimated) timings of the campaign? (i.e. start and end date) - Resources (financial & human resources): Financial resources - refers to the estimated cost/budget for the campaign. Human resources – i.e. in-house or creative agency? - Results & Evaluation: State the campaign results achieved. How was the campaign’s success measured or evaluated? Section B: 500 words Based on your analysis in Part A, recommend how the brand can improve the effectiveness of the campaign. You must use relevant Marketing Communications theories to justify your suggestions. Helpful Information Details about advertising campaigns are available via trade magazine websites (e.g. Marketing, Marketing Week, The Drum, PR Week, Campaign, Brand Republic etc.) You should include pictures/copies of the brand’s advertising/PR and other promotional tools within your report. Please ensure these are referenced. Word Count The total word count for both sections is 2,000 (both sections must be completed). The word limit includes quotations but excludes the references/bibliography. How to submit your assessment The assessment must be submitted by the due date as stated. No paper copies are required. You can access the submission link through the module folder on Blackboard. • Your coursework will be given a zero mark if you do not submit a copy through Turnitin on Blackboard. Please take care to ensure that you have fully submitted your work. • Please ensure that you have submitted your work using the correct file format, unreadable files will receive a mark of zero. The University accepts Microsoft Office and PDF documents, unless otherwise advised by the module leader. • All work submitted after the submission deadline without a valid and approved reason (see below) will be given a mark of zero. • If you would like to apply for a slight extension, you must apply before the deadline with a valid reason and supporting copies of documentation. • If you need a considerable amount of extension, you may apply for a deferral, which takes you to the next assessment period (for example, to the resit period following the main Assessment Boards). You will find information about the process and what is or is not considered to be an event beyond your control at https://share.coventry.ac.uk/students/Registry/Pages/Deferrals-and-Extension.aspx • Students MUST keep a copy and/or an electronic file of their assignment. • Checks will be made on your work using anti-plagiarism software and approved plagiarism checking websites. Plagiarism As part of your study you will be involved in carrying out research and using this when writing up your coursework. It is important that you correctly acknowledge someone else’s writing, thoughts or ideas and that you do not attempt to pass this off as your own work. Doing so is known as plagiarism. It is not acceptable to copy from another source without acknowledging that it is someone else’s writing or thinking. This includes using paraphrasing as well as direct quotations. You are expected to correctly cite and reference the works of others. The Centre for Academic Writing provides documents to help you get this right. If you are unsure, please visit www.coventry.ac.uk/caw. Self-plagiarism or reuse of work previously submitted You must not submit work for assessment that you have already submitted (partially or in full), either for your current course or for another qualification of this and any other university, unless this is specifically provided for in your assignment brief or specific course or module information. Where earlier work by you is citable, i.e. it has already been published/submitted, you must reference it clearly. Identical pieces of work submitted concurrently will also be considered to be self-plagiarism. Self-plagiarism is unacceptable because you cannot gain credit for the same work twice. Blackboard includes a plagiarism detection system and assessors are experienced enough to recognise plagiarism when it occurs. Copying another student’s work, using previous work of your own or copying large sections from a book or the internet are examples of plagiarism and carry serious consequences. Please familiarize yourself with the APA Reference Style (on Blackboard) and use it correctly to avoid a case of plagiarism or cheating being brought. If you are unsure, please contact the Centre for Academic Writing, or a member of the course team. Coursework 2: Advertising Plan (50%) - Group Learning Outcomes Assessed by this Assignment 1. Define and evaluate appropriate measures for evaluating marketing communications activities 2. Develop an advertising plan using a range of creative ideas to meet a specific advertising brief 3. Present and justify advertising ideas according to audience, messages and media criteria Summary This assignment allows you to showcase your presentation and delivery skills. You will showcase the necessary content to experience the skills involved in a pitch. Consideration to content, delivery, pitch angle and choice of strategy will be tested in this component. Assignment Description For this group coursework, each team will act as the creative agency pitching an advertising campaign for potential client, Impossible Foods. Your lecturer will discuss the details of the client brief in class. Each group is expected to plan an IMC campaign to address stipulated objectives including promoting one of the client’s products strategically across different media platforms to increase sales. Your pitch (using PPT slides) must include the following: 1. Introduction of creative agency and client organization 2. Situational analysis a. identification of key issues in the macro or microenvironment which may impact the client (consider SWOT or PESTLE) b. justification for proposed campaign 3. Introduction of proposed campaign (i.e. campaign name, slogan and duration) 4. Campaign objective/s 5. Target audience 6. Core message/s 7. Strategies and Tactics (including communication tools, ad appeal and executional framework strategies, media channels, advertising design and copy) 8. Implementation schedule 9. Campaign evaluation methods 10. Estimated budget 11. References Submission Requirements Your slides for this assignment will be submitted by 2359hours on the stipulated date via the Turnitin link on the module folder on Blackboard. You must include the full name of all group members in your submission. Word Count Your presentation must be within 15-20 minutes with approximately 20 slides. The group presentation will consist of an individual Q&A. Word count for the notes section is not applicable however your notes should be detailed enough to explain each slides content in detail. There will be a penalty of a deduction of 10% of the mark (after internal moderation) for presentations exceeding the presentation time limit. How to submit your assessment The assessment must be submitted by the due date as stated. No paper copies are required. You can access the submission link through the module folder on Blackboard. • Your coursework will be given a zero mark if you do not submit a copy through Turnitin on Blackboard. Please take care to ensure that you have fully submitted your work. • Please ensure that you have submitted your work using the correct file format, unreadable files will receive a mark of zero. The University accepts Microsoft Office and PDF documents, unless otherwise advised by the module leader. • All work submitted after the submission deadline without a valid and approved reason (see below) will be given a mark of zero. • If you would like to apply for a slight extension, you must apply before the deadline with a valid reason and supporting copies of documentation. • If you need a considerable amount of extension, you may apply for a deferral, which takes you to the next assessment period (for example, to the resit period following the main Assessment Boards). You will find information about the process and what is or is not considered to be an event beyond your control at https://share.coventry.ac.uk/students/Registry/Pages/Deferrals-and-Extension.aspx • Students MUST keep a copy and/or an electronic file of their assignment. • Checks will be made on your work using anti-plagiarism software and approved plagiarism checking websites.
MATH2003J, OPTIMIZATION IN ECONOMICS, BDIC 2023/2024, SPRING Problem Sheet 6 Question 1: Solve the following LP problem by the simplex method: Minimize z = 3x1−2x2 subject to x1 − x2 ≤ 1, x1 − x2 ≥ −2, x1, x2 ≥ 0. Question 2: Solve the following LP problem by the simplex method: Maximize z = 8x1 + 2x2+2x3 subject to 2x1 + x2 + 4x3 ≤ 60, −x2 − x3 ≤ −40, x1, x2, x3 ≥ 0. Question 3: Solve the following LP problem by the simplex method: Maximize z = 4x1+5x2 subject to x1 + 2x2 ≤ 20, x1 + x2 ≤ 18, 2x1 + x2 ≥ 12, x1, x2 ≥ 0. Question 4: Solve the following LP problem by the simplex method: Minimize z = 2x1 − 3x2+x3 subject to 2x1 − x2 + 3x3 ≤ 7, −4x2 + 2x3 ≥ 12, 8x1 + 3x2 − 4x3 ≤ 10, x1, x2, x3 ≥ 0. Question 5: Solve the following LP problem by the simplex method: Minimize z = x1 + x2 + 2x3 subject to x1 + 2x2 − x3 ≥ 8, x1 + x2 − 2x3 ≤ 10, x1, x2, x3 ≥ 0. Question 6: Solve the following LP problem by the simplex method: Maximize z = 5x1 + 4x2 subject to 2x1 + x2 ≤ 20, x1 + x2 ≤ 18, x1 + 2x2 = 12, x1, x2 ≥ 0. Question 7: Solve the following LP problem by the simplex method: Maximize z = 2x1 − 3x2 subject to x1 + x2 ≤ 10, x1 − x2 ≤ 12, 2x1 − x2 ≥ 6, x1 ≥ 0. Question 8: Solve the following LP problem by the simplex method: Minimize z = 2x1 + 3x2 subject to − x1 + x2 ≤ 10, −x1 − x2 ≤ 12, −2x1 − x2 ≥ 6, x1 ≥ 0, x2 ≤ 0. Question 9: Solve the following LP problem by the simplex method: Minimize z = x1 + x2 subject to 2x1 + x2 ≥ 16, x1 + 2x2 ≥ 20, x1, x2 ≥ 0.
F24 ECE 551 HW02, Due 11PM Thu. Sep. 19 Pr. 1. (a) Prove how the eigenvalues and eigenvectors of B ≜ A − 10I relate those of A ∈ F N×N . (b) Describe (without proof) how the eigenvalues and eigenvectors of B ≜ αI +βA +γA2 relate to those of A ∈ F N×N . (c) Describe (without proof) how the eigenvalues and eigenvectors of B ≜ (αA + βI) −1 relate to those of A ∈ F N×N , assuming the matrix in parentheses is invertible. Hint. If A is invertible and Ax = λx, then multiplying both sides by (1/λ)A−1 yields (1/λ)x = A−1x. Pr. 2. Let v1, v2, . . . , vN denote orthonormal vectors in R N . Let B denote the set of vectors {Av1, Av2, . . . , AvN } for A ∈ R N×N . (a) Show that if A is an orthogonal matrix, then B is an orthonormal set. (b) Show the converse: if B is an orthonormal set, then A is an orthogonal matrix. Pr. 3. The Frobenius norm of an M × N matrix A is defined as Express the Frobenius norm of A in terms of its singular values. Hint: First express |||A|||F in terms of the matrix A′A. Pr. 4. Let A be an M × N matrix with spectral norm σ1. Show the following bounds on the Frobenius norm: The operator norm of a matrix equals its largest singular value σ1. The norm of a matrix can be measured many ways. The above inequality shows that if the Frobenius norm is small then the operator norm is as well. However, the operator norm being small does not guarantee that the Frobenius norm will be as well. (Think, for example, of the setting when M and N are very large). Optional challenge: Is the upper bound tight? Pr. 5. The Kronecker product of two matrices A ∈ F m×n, B ∈ F k×l is an important form. of “matrix multiplication” defined as follows: Let vec(X) denote the “vectorize” operation that returns as its output a vector in FMN formed by stacking the N columns of X ∈ FM×N on top of each other. For vectors x ∈ FM and y ∈ F N , so that xy⊤ ∈ FM×N , prove that Verify (for yourself) by using commands vec(x * y’) and kron(y, x) in Julia for some real vectors, and using vec(x * transpose(y)) for some complex vectors. (The equality above does not hold for vec(xy′ ) when y is complex.) Pr. 6. Use an SVD of a square matrix A to describe a factorization A = QS where Q is unitary and S is positive semidefinite. Express Q and S in terms of the SVD components U, Σ and V of A. Show that your Q and S satisfy the requirements. (This matrix decomposition is analogous to the polar form. z = reiθ of a complex scalar z, where r is like S and e iθ is like Q.) Hint: V ′V = I, so XY = XIY = XV ′V Y for compatible matrices. Pr. 7. We use the notation F to denote either the field R of real numbers or the field C of complex numbers. This problem reviews what a field is. (See Ch. 1.) Determine whether the following sets (with the usual senses of multiplication, addition, etc.) are fields or not. If the answer is Yes then you may say so without proof. If the answer is No then give a concrete counterexample for one of the defining properties of a field that is violated. (a) The set of numbers that are irrational or zero, i.e., the set (R − Q) ∪ {0} (b) The set of N × N diagonal matrices (where the “1” element is IN , and the “0” element is 0N×N ). (c) The set of N × N diagonal matrices whose diagonal elements are either all zero or all nonzero. (d) The set of rational functions, i.e., functions of the form. P(x)/Q(x) where P and Q are both polynomials (over the same field F) and Q is not zero. (e) The set of N × N invertible matrices along with the N × N zero matrix. Pr. 8. (a) Determine how eigenvalues and eigenvectors of are related to singular values and singular vectors of A ∈ F N×N . In other words, if A = UΣV ′ , then express eigenvalues and eigenvectors of B in terms of components of U, Σ and V . Hint. Start with some numerical experiments using self-generated A matrices and form. a conjecture. Note that B is 2N × 2N. Think about combining ui and vi in various ways, such as ui ± vi , , and . (b) Optional. Write a unitary eigendecomposition of B in matrix form. (c) Optional. Generalize to the case A ∈ FM×N for M ≥ N. This problem is related to one SVD numerical approach. Pr. 9. Your graduate school experience should be more than just taking courses. To convince you that we really mean that, you have the opportunity to earn 30 HW points by writing down some of your own non-course-related goals for this semester. Thinking beyond courses is especially important in this (hopefully) post-pandemic period where self-care is crucial. In a few sentences or bullet points, list some of your personal non-course goals for this semester. The intent of this assignment is to encourage you to practice good self-care and encourage a growth-mindset. Examples of activities someone might list would be: going on a walk in your neighborhood N times a week, making connections with N new people, attending N CSP seminars to learn about current research, exploring some topic beyond what is required in the course just for your own interest, mastering a new recipe, reading a novel, etc. Hopefully your list will include some things that will help you relax and/or think about the bigger picture. There will be another HW problem at the end of the semester where we will ask you to reflect on your goals for the semester. If what you did was different than your proposal, please tell us what you ended up doing. Obviously we will never know if you actually read that novel or not. This is really for you to be thinking about. Pr. 10. (Finite difference matrix) This problem develops a tool that will be used in a later HW for an application called photometric stereo. To approximate the derivatives of a function f(x) that is sampled on the grid x1, . . . , xn where xi+1 = xi + δ, a typical finite difference approach is: When the sample spacing is δ = 1, this approximation simplifies to We can express this relation for all xi samples via the matrix-vector product where Dn is the so-called first finite difference matrix defined by Here we choose to set Dn[n, 1] = 1, which corresponds to the (perhaps unexpected) approximation f ′ (xn) ≈ f(x1) − f(xn). This choice is called a periodic boundary condition because essentially we are assuming that the domain wraps around. We make this assumption because the resulting Dn is a circulant matrix so its eigenvectors can be computed in closed form! (See Ch. 8.) The goal of this problem is for you to derive and implement the analog of Dn for 2D differentiation. Let f(x, y) be a function of two variables. We can approximate its partial derivatives using finite differences as follows: To simplify notation, define the m × n matrices FXY, DFDX, and DFDY having elements as follows: The x coordinate is along the column of FXY and the y coordinate is along the row of FXY, so we can think FXY[x,y]. Define corresponding vectors fxy, dfdx, and dfdy in R mn to be vectorized versions of FXY, DFDX, and DFDY. With this notation, we can succinctly express equations (1) and (2) as where A is a 2mn × mn matrix. To help explain the notation, here is a concrete example: (a) Find an expression for A in terms of the first difference matrices Dn, Dm, appropriately sized identity matrices, and appropriate Kronecker products of these matrices. Use periodic boundary conditions. Hint: Start with m = n = 3. Look for ways to use Kronecker product(s) and the vec trick. Hint: To make a 5 × 5 identity matrix use: using LinearAlgebra: I I(5) (b) Once you have determined A, write the function first_diffs_2d_matrix that takes as input the dimensions m and n of FXY and returns the appropriate A matrix, stored in sparse format. In Julia, your file should be named first_diffs_2d_matrix.jl and should contain the following function: """ A = first_diffs_2d_matrix(m, n) # In: - `m` and `n` are positive integers # Out: - `A` is a `2mn × mn` sparse matrix such that `A * vec(X)` computes the first differences down the columns (along x direction) and across the (along y direction) of the `m × n` matrix `X`. """ function first_diffs_2d_matrix(m, n) Email your solution as an attachment to [email protected]. Hint. Be sure to have using [packagename] at the top of your code for any package you use. The matrix A can be gigantic. For example, suppose m = 550 and n = 430, then A is a 473, 000 × 236, 500 matrix that would require 833 GB of RAM if stored as a full double precision matrix! However, A has only 4mn nonzero entries, so it is very sparse. Matrices with many zero-valued elements are quite common in applications. For normal arrays, Julia (and other languages) stores zeros in the same way it stores other numeric values, so having many zero elements can use memory space unnecessarily and can sometimes require extra computing time. Sparse matrices provide an efficient way to store data that has a large percentage of zero elements. While full matrices internally store every element in memory regardless of value, a sparse matrix data structure stores only the nonzero elements and their row indices. Using sparse matrices can significantly reduce the amount of memory required for data storage. In Julia, to create a sparse matrix somewhat similar to Dn above one can use either the spdiagm command: using SparseArrays n = 5 A = spdiagm(0 => 1:n, -1 => ones(n-1)) or a loop: n = 5 A = spzeros(n,n) for i in 1:n-1 A[i,i], A[i,i+1] = i, 1 end You should try one or both of these out and modify one of them to prepare your answer. For details, see the SparseArrays documentation. For any Julia assignment, you should always try to think of your own ways of testing your function before submitting to the auto-grader. You do get unlimited tries with the auto-grader, but using the feedback from the auto-grader is a poor way to debug. By designing your own tests, you can examine their output interactively and fix bugs more intelligently. In this problem your function is designed to compute finite difference approximations to derivatives along x and y. If you create a m × n array X that is, say, a picture of a disk, then the finite derivatives will be mostly zero except near the edges of the disk. (This property is related to an image processing application called edge detection that is discussed in EECS 556.) Here is Julia code for making a (digital/sampled) disk and showing pictures of FXY, DFDX, DFDY. using MIRTjim: jim using Plots: savefig m = 30; n = 20; X = Float64.([(x-12)^2+(y-8)^2 < 5^2 for x in 1:m, y in 1:n]) dfdx = diff(X; dims=1) dfdy = diff(X; dims=2) jim( jim(X, "FXY: f(x,y)"; xlabel="x", ylabel="y"), jim(dfdx, "DFDX: df(x,y) / dx"; xlabel="x", ylabel="y"), jim(dfdy, "DFDY: df(x,y) / dy"; xlabel="x", ylabel="y"), ) # savefig("hp074_disk.pdf") You should make similar examples to test your function.
