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Assignment Problem for Business 2400

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(i) For general instructions about assignments, please see Section 3 of the Course Outline, especially Section 3.3 on file formats.

(ii) This document has been created only for internal use at Memorial University. This pdf file is not to be forwarded to anyone not currently registered in Business 2400. Any transmission of the solutions to this assignment to a third party constitutes academic dishonesty.

An electronics shop is about to buy some high-definition televisions (HDTVs). While these have 4K resolution, they do not have any advanced features such as HDR, QLED, or OLED. They can be ordered from the manufacturer at a cost of $210 each. The selling price will be set at $300 each. Demand is estimated as being between 11 and 16 inclusive with probabilities 0.15 for 11, 0.2 for 12, 0.3 for 13, 0.25 for 14, 0.08 for 15, and 0.02 for 16. After this purchase, they will only order higher-quality 4K and 8K resolution HDTVs; any leftover of these low-end 4K TVs will be marked down to $180 each (all leftover stock will sell with no problem at this price)

All parts (a) to (f) may be done either by hand or by using Excel.

Make a table by hand or an Excel worksheet, in which each alternative is in a row, and each outcome is in a column. Note: This is like the problem in Section 8.3.3 of the textbook, for which solutions are provided on the Business 2400 Brightspace site. For each alternative and outcome, calculate the possible payoffs.

To the right of part (a), create columns to determine a recommendation using each of the following criteria: (i) expected value, (ii) pessimism, (iii) optimism, (iv) Hurwicz using a coefficient of pessimism of 0.7, and (v) Laplace. (c) Verify (b) (i) using the marginal analysis formula. (d) Find the EVPI. (e) Find the payoffs of the regret matrix. (f) Calculate the EOL column, and verify the solution to (d). Business 2400, Fall 2021, written by Dr. David M. Tulett 2

In the Spring of 2021 a concert promoter is planning a single performance of a distinguished pianist playing suites for keyboard written by G.F. Handel. Several venues are being considered, all of which have a grand piano, and are accessible for those with physical challenges. Because of the COVID-19 pandemic, which causes a need for physical distancing, each venue can only admit 25% of its seating capacity. For example, while the Cathedral has a capacity for 1000 people in normal times, during the pandemic only 250 people may be admitted. Each venue charges a rental fee, plus a cleaning surcharge per person in attendance beyond a threshold number. For example, suppose they rent the Basilica, and 265 people show up. The threshold is 225, so they pay a cleaning surcharge based on 265−225 = 40 people.

Developing their own vaccine would cost (all figures are in USD) 900 million, and would have a 40% chance of being successful (i.e. taking the vaccine would actually prevent infection by the virus). However, it would then need extensive testing to make sure that there are no (or at worst, few) unintended side effects. Depending on what is discovered during the development of the vaccine, there’s a 15% chance of needing extensive testing, and an 85% chance of needing only ordinary testing.

The company could abandon the project just before testing if it wished to do so. Extensive testing would cost 2000 million, and there’s a 65% chance that the drug could be rejected at this stage. Ordinary testing would cost 500 million, and there’s a 30% chance that the drug could be rejected at this stage. The company believes that a vaccine with few side effects would be worth 10,000 million in future gross profit. Partnering with the university has some pluses and minuses. On the one hand, development costs would be only 750 million, and the probability of success in protecting against the virus would be 80%. On the other hand, the university would stipulate that they would have to market the vaccine only slightly above cost per vaccine. Even so, worldwide demand would be so great that the gross profit would still be a respectable 5000 million. The probability of needing extensive testing is now only 10% (and therefore the probability of needing ordinary testing is 90%), but the other testing costs and probabilities are the same as in the preceding paragraph. Again, the company could abandon the project just before testing if it wished to do so.