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 upon the demand for the

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 upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars):

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

1. Use a decision tree to recommend a decision.
   
   Recommended decision: 
   
   
2. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.
   
   EVPI: $  f
   
   
3. 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? If required, round your answer to three decimal places.
   
   P(F) =