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e. The value of a perfect forecast is given by the EVPI. First calculate the following;EV with PI = (85)0.2 + (100)0.3 + (120)0.5 = 107EVPI = (EV with PI) – (Best EMV without PI) = 108 – 107 = 1Thus, a perfect forecast is worth 1 (thousand).f. The location that minimizes the EOL is Sweetwater.g. The expected value of perfect information (EVPI) is 1. This is found in part e, and it is also the minimum EOL.
6Problem 6A group of medical professionals is considering the construction of a private clinic. If the medicaldemand is high (i.e., there is a favorable market for the clinic), the physicians could realize a net profit of$100,000. If the market is not favorable, they could lose $40,000. Of course, they don't have to proceed at all,in which case there is no cost. In the absence of any market data, the best the physicians can guess is thatthere is a 50-50 chance the clinic will be successful. Construct a decision tree to help analyze this problem.What should the medical professionals do? EMV for node 1 = 0.5(100,000) + 0.5(–40,000) = $30,000. Choose the highest EMV, therefore construct theclinic.Problem 7The physicians in Problem 6 have been approached by a market research firm that offers to perform astudy of the market at a fee of $5,000. The market researchers claim their experience enables them to useBayes' theorem to make the following statements of probability: probability of a favorable market given a favorable study = 0.82 probability of an unfavorable market given a favorable study == 0.18 probability of a favorable market given an unfavorable study = 0.11 probability of an unfavorable market given an unfavorable study = 0.89 probability of a favorable research study = 0.55 probability of an unfavorable research study = 0.45 (a) Develop a new decision tree for the medical professionals to reflect the options now open with themarket study. (b) Use the EMV approach to recommend a strategy. (c) What is the expected value of sample information? How much might the physicians be willing topay for a market - study? (d) Calculate the efficiency of this sample information. a.
7b. EMV(node 2) = (0.82)($95,000) + (0.18)(–$45,000)= 77,900 – 8,100 = $69,800EMV(node 3) = (0.11)($95,000) + (0.89)(–$45,000)= 10,450 – $40,050 = –$29,600EMV(node 4) = $30,000EMV(node 1) = (0.55)($69,800) + (0.45)(–$5,000)= 38,390 – 2,250 = $36,140The EMV for using the survey = $36,140.EMV(no survey) = (0.5)($100,000) + (0.5)(–$40,000)= $30,000The survey should be used.c. EVSI = ($36,140 + $5,000) – $30,000 = $11,140.Thus, the physicians would pay up to $11,140 for the survey.Problem 8. Bayesian Analysis
8Peter Martin is 'going to help his brother who wants to open a food store. Peter initially believes thatthere is a 50-50 chance that his brother's food store would be a success. Peter is considering doing a marketresearch study. Based on historical data, there is a 0.8 probability that the marketing research will befavorable given a successful food store. Moreover, there is a 0.7 probability that the marketing research willbe unfavorable given an unsuccessful food store. (a) If the marketing research is favorable, what is Peter's revised probability of a successful food storefor his brother?