# solution

The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent on the demand for the product. The following payoff table shows the projected profit (in thousands of dollars):

 State of Nature Low Demand Medium Demand High Demand Decision Alternative s 1 s 2 s 3 Manufacture, d 1 -20 40 100 Purchase, d 2 10 45 70

The state-of-nature probabilities are P(s1) = 0.50, P(s2) = 0.40, and P(s3) = 0.10

(a) Use a decision tree to recommend a decision.
(b) Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. Enter your answer in thousands dollars. For example, an answer of \$200 thousands should be entered as 200,000.
Gorman – Select your answer -shouldshould notItem 2 attempt to obtain a better estimate of demand, as the additional information could be worth up to \$ for Gorman.
(c)

A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:

 P(F|s1) = 0.10 P(U|s1) = 0.90 P(F|s2) = 0.40 P(U|s2) = 0.60 P(F|s3) = 0.60 P(U|s3) = 0.40

What is the probability that the market research report will be favorable? [Hint: We can find this value by summing the joint probability values as follows: P(F) = P(Fns1) + P(Fns2) + P(Fns3) = P(s1)P(F|s1) + P(s2)P(F|s2) + P(s3)P(F|s3) .] If required, round your answer to three decimal places.

(d) What is Gormanâ€™s optimal decision strategy? Choose the correct option.
 A. Conduct test market, and manufacture component part, regardless of the market research report B. Conduct test market, and purchase component part, regardless of the market research report C. Conduct test market, and manufacture component part if market is favorable, or purchase component part if market is unfavorable D. Do not conduct test market, and purchase component part E. Do not conduct test market, and manufacture component part