25.                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 re- sulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars):

 

Â	    Low Demand	State of Nature Medium Demand	    High Demand
Decision Alternative	s1	s2	s3
Manufacture, d1	-20	40	100
Purchase, d2	10	45	70

 

The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30.

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.

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 ƒ s1) = 0.10 P(F ƒ s2 ) = 0.40 P(F ƒ             s3) = 0.60

 

P(U ƒ s1) = 0.90 P(U ƒ s2 ) = 0.60 P(U ƒ             s3) = 0.40

 

 

What is the probability that the market research report will be favorable?

d.             What is Gorman’s optimal decision strategy?

e.              What is the expected value of the market research information?

f.               What is the efficiency of the information?