Question

5. The Gorman Manufacturing Company decides to manufacture a component part at its Milan, Michigan plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand of the product. The following payoff table shows the projected profit (in thousands of dollars) State of Nature Low Demand Mediumm Demand High Demand Decision Alternative Manufacture, d1 -20 40 100 Purchase, d2 10 45 70 The state probabilities are as follows: P(s3) 0.30 P(%) 0.35, P(82)-0.35, and A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows P(FIs1) 0.10 P(FIs2) 0.40 P(FIs3)0.60 PCUls,) 0.90 P(U s2) 0.60 PCUİSg)-0.40 Use Bayes' theorem for probability revision to compute the probability of each condition, F and U, and the conditional probabilities of low demand (s1), medium demand (s2), and high demand (s3), given each condition (F and U) a. b. Show the decision tree for this problem What is P(F) and P(U), the respective probabilities that a market research report will be favourable (F) and unfavourable (U) c. d. What is the optimal decision strategy, and what is the expected profit? e. Develop a risk profile for the optimal strategy before (prior) and after (posterior) the market research. What conclusion do you draw from this risk profile? Continued. /7

Answer 1

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