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Business 36106 (Autumn 2023) Final (Solutions) 36106: Managerial Decision Modeling Autumn 2023 FINAL (Solutions) December 2023 May the force be with Harry Q. Bovik I pledge my honor that I have not violated the Chicago Booth Honor Code during this examination. I have not shared, transmitted or received written or electronic answers with/to/from other classmates. (Sign): H.Q. Bovik Q1 (7 pts) Q2 (5 pts) Q3 (7 pts) Q4 (11 pts) TOTAL (30) Instructions 1. This is a timed exam with 72 hour duration . You will have 72 hours from the time you accessed this exam to upload your submission. However, you should submit your exam no later than 11:59 pm on Thursday, December 7, 2023 . 2. There are 4 questions and 13 numbered pages. Maximum possible score is 39. 3. The information contained in this documents is confidential, privileged and only for the information of the intended recipient and may not be used, published or redistributed without the prior written consent of the instructor. 4. This exam is to be done individually. You are not to receive help from or give help to others. There should be no discussion of the exam or the topics covered, nor any discussion of course- related software, nor any sharing of course or exam-related files, between the time you download the exam and the time you hand in your completed work. You may not discuss this exam with anybody who has not already completed it. 5. You may not save any exam-related files on shared disk space and may not access others’ exam- related files. 6. This exam is open book and open notes. This means that you may use your course cases, handouts, notes, and assignments received and/or produced while taking this course. You may i

Business 36106 (Autumn 2023) Final (Solutions) access course files (slides, examples, etc.) posted on Canvas during the exam. You may not use notes or materials from this course (or similar courses) in other years or in other programs. You may not use any materials from the internet other than those posted on Canvas. 7. Do not post information or ask questions related to the exam or course to any electronic bulletin board, forum, or discussion group (or on Facebook, twitter, etc.) during the period of the exam. 8. Answer sheets: Scan and upload your answer sheets to Canvas by the deadline. You can also use any pdf editing software to type your solutions. You can insert extra pages if you need more space to write your answers, or to include screenshots of your results. Upload a single pdf file, and make sure that your pdf is readable by Adobe Acrobat. If you are running out of time in scanning your answersheet, upload photos of the answersheet, and email us your pdf answersheet within 24 hours. 9. Excel files: Download the excel files from Canvas or create a new file as indicated in the questions, implement your Solver/PrecisionTree/RISK models in them, and upload these files with your answersheet to Canvas by the deadline. 10. Write your answers in the space indicated. Where asked for constraints or objective function, write a very short English description followed by a precise mathematical expression. Example: Capacity constraint for Plant 1 : X 11 + X 12 + X 13 ≤ 4000 Rambling, unfocused qualitative answers will be penalized. 11. For your @RISK simulations, unless specified, choose number of iterations as 1000. It is encouraged that you include screenshots of your simulation outputs (e.g., histograms, RiskSimTable outcomes) in either your uploaded Excel workbooks, or in your answersheet. ii

Business 36106 (Autumn 2023) Final (Solutions) 1 LLC’s Strategic Alliance Problem [7 pts] Create a file LLC Strategic alliance.xlsx . Build any PrecisionTree models in this workbook and upload with the rest of your submission. As she was driving home Friday evening, Yiduo Chen, Vice President of Sales & Marketing at Lexing- ton Laser Corporation (LLC), kept thinking about the interesting opportunity she had stumbled upon during last week’s west-coast business development trip. It seems that Aspen Networks, an emerging company in the network business, has a requirement for a custom laser transmitter for one of their new transmission systems. Because Aspen’s strength is in communications systems and not in opto-electronic components, they indicated that they are interested in forging a strategic supply arrangement with LLC (or perhaps some other opto-electronic component manufacturer) for the supply of custom laser transmitters. Aspen is confident that they can carve out a leadership position in the market with their new system which could translate into 10 million in laser transmitter orders for LLC over three years. Yiduo was definitely excited about this potential opportunity for LLC. After reviewing the technical specifications for the custom part with Peter Williams (VP of Engineering), it appeared that with minimal engineering investment LLC could adapt one of their existing designs to obtain the requisite functionality. Yiduo then started working with the manufacturing folks: Julie Weller (VP of Manufacturing) and Steve Lo (Manufacturing Engineering Manager). Julie and Steve felt that although there was sufficient excess capacity at LLC to produce the required laser chips, the rest of the manufacturing process for the custom lasers would require establishing a small dedicated manufacturing line at a cost of 800,000. It would take four months to build this facility – just three months before LLC would expect the first orders from Aspen. Yiduo then tried to look more carefully at the numbers. The Aspen management team was optimistic that they could capture enough business to provide LLC with orders for 10,000 lasers over three years. Indeed, at a price of 1,000 per laser (giving the 10 million revenue mentioned earlier) and 20% after- tax profit margins, this opportunity seemed profitable. However, as Yiduo studied the network market a bit closer, she learned that while Aspen had some leading edge technologies and a novel approach, Aspen also had two established competitors, and the optimistic scenario above may not materialize. Yiduo also thought that given the rapid pace of technological innovation and commercialization in the communications industry, this custom laser would most probably have a relatively brief lifecycle of three years, and that much of the dedicated manufacturing facility would not have an alternate use beyond the third year. With input from Aspen and their customers, Yiduo estimated the best-case and worst- case revenues (corresponding to the range of Aspen’s acceptance in the market) and post-tax profit projections as follows: Best-case: Year 1 revenue 2 million, Year 2 revenue 5 million, Year 3 revenue 3 million. This gave a total revenue of 10 million over three years yielding after-tax profits (excluding the cost of setting up the dedicated manufacturing line) of 2 million. Worst-case: Year 1 revenue 0.5 million, Year 2 revenue 1.25 million, Year 3 revenue 0.75 million. This gave a total revenue of 2.5 million over three years yielding after-tax profits (excluding the cost of dedicated manufacturing line) of 0.5 million. 1

Business 36106 (Autumn 2023) Final (Solutions) The probability of “Best-case” is subjectively estimated to be 70%. At a meeting with the Aspen team, Yiduo explained her company’s reluctance to invest in a custom manufacturing facility with an uncertain future. Hank Philips (purchasing manager of Aspen) then explained that Aspen has also been talking with another laser manufacturer to explore contract manu- facturing of custom lasers. Although LLC was Aspen’s first choice, the other manufacturer had already committed the resources for a dedicated line, and Aspen had even placed preliminary orders. Yiduo then brought up the possibility for LLC to wait six months prior to committing to the dedicated line, in order to see how Aspen’s new system fares in the marketplace. Hank explained that while they would be willing to work with LLC for the following two years, the laser orders they would place with LLC for years two and three would then be smaller by approximately 30%. That is, Best-case under strategy of waiting six months before committing: Year 1 revenue 0, Year 2 revenue 3.5 million, Year 3 revenue 2.1 million. Worst-case under strategy of waiting six months before committing: Year 1 revenue 0, Year 2 revenue 0.875 million, Year 3 revenue 0.525 million. While the revenue opportunity was lower in the more conservative approach of waiting six months prior to building the line, it would allow LLC to know exactly whether Aspen would be successful (“best-case”) or not (“worst-case”) in the marketplace. In the event Aspen was not successful, LLC would be spared the investment in a manufacturing facility that would not pay for itself. As Yiduo drove home, she mulled over the options. Build the facility or not? Hold off for six months to see whether Aspen is successful? (a) [1 pts] What is the expected payoff (including the cost to setup the facility) if LLC decides to go ahead with the alliance with Aspen now? Assume a discount rate of 0% throughout this ques- tion. You need not create a PrecisionTree model for this question, but you should explain your calculations. Answer: There is an immediate cost of 800,000 to set up the facility; and subsequently a profit of 2 million with 70% chance and 0.5 million with 30% chance. Overall expected payoff = − 0 . 8 + (0 . 7 × 2 + 0 . 3 × 0 . 5) = 0 . 75 million . (b) [1 pts] What is the expected payoff if LLC decides to wait 6 months? You need not create a PrecisionTree model for this question, but you should explain your calculations. Answer: If Aspen will be successful, the profit for LLC would be 0 . 2 × (3 . 5 + 2 . 1) = 1 . 12 million, therefore in this Aspen would invest the fixed cost in setting up the facility. If Aspen will be unsuccessful, LLC will not form the alliance and payoff would be 0. Overall expected payoff = 0 . 7 × ( − 0 . 8 + 1 . 12) + 0 . 3 × 0 = 0 . 224 million . 2

Business 36106 (Autumn 2023) Final (Solutions) (c) [1 pts] The chance of Aspen’s success p success = 70% was a subjective estimate. LLC would like to know at what value for the chance of success of Aspen would the expected payoffs under the “proceed now” and “wait 6 months” options be equal. You need not create a PrecisionTree model for this question, but you should explain your calculations. Answer: The payoff if LLC proceeds now is = − 0 . 8 + 2 p + 0 . 5(1 − p ) and if LLC waits is = p ( − 0 . 8 + 1 . 12) = 0 . 32 p. Equating the two, we get p = 0 . 8 − 0 . 5 1 . 5 − 0 . 32 = 0 . 3 1 . 18 = 0 . 254 . That is, if Aspen’s probability of success is higher than 25.4% then LLC should go ahead with the alliance now instead of waiting (assuming LLC is risk neutral and expected payoff maximizer). (d) [1 pts] Suppose LLC could access perfect forecast about Aspen’s success/failure in the mar- ketplace, how much should LLC be willing to pay for this forecast? You need not create a PrecisionTree model for this question, but you should explain your calculations carefully. Answer: With perfect forecast, LLC would have a payoff of − 0 . 8 + 2 = 1 . 2 million in the case Aspen is successful and a payoff of 0 if Apsen is not successful. The expected payoff would be 0 . 7 × 1 . 2 = 0 . 84 million. Without this perfect forecast, the optimal decision for LLC is to form an alliance now, with an expected payoff of 0 . 75 million. Therefore the value of this perfect forecast is 0 . 84 − 0 . 75 = 0 . 09 million, or $90 , 000 . (e) [3 pts] Yiduo called her friend Frank Sullivan, who runs a market research firm focusing in fiber optic communications and networking. Frank was well-versed in the dynamics of Aspen’s market, and he seemed to have a good sense of their target customers. He felt that by putting three analysts on the problem for two months, his company could give Yiduo an excellent assessment of Aspen’s prospect in this market. The study would cost LLC 150,000. Of course, Yiduo was not as excited as Frank was about commissioning a market research study. Yiduo’s previous experience indicated that such predictions are wrong 30% of the time. That is, if the true outcome would have been ‘success’, the prediction would be ‘success’ only 70% of the time, and if true outcome would been ‘not successful’ the prediction would be ‘not successful’ only 70% of the time. Should Yiduo commission the study? Build a Precision Tree model to solve for Yiduo’s optimal strategy given she commissions the study, and use the solution to answer this question. Hint: You first need to compute the probabilities that the study will report the outcomes as ‘success’ or ‘not successful’ based on the information above. From these, you then need to compute the probability that the true outcome is ‘success’ given that the report says ‘success’ using elementary probability. 3

Business 36106 (Autumn 2023) Final (Solutions) Answer: The optimal tree is given below. The optimal decision given either market report is to continue with alliance now, which is also the decision without the market report. Therefore there is no value for this imperfect forecast. 4

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