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

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
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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):

 

  State of Nature
  Low Demand 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.

 

  1. Use a decision tree to recommend a decision.

    Recommended decision:
     

 

  •  


  • Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.

     
  •  


    EVPI: $  fill in the blank 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) = fill in the blank 4

  • What is Gorman's optimal decision strategy?

    Decision strategy:

    If F then
     

 

 

.

If U then

 

 

  •  
    .

  • What is the expected value of the market research information?

    Expected value: $  fill in the blank 7

  • What is the efficiency of the information? If required, round your answer to one decimal place.

    Efficiency: fill in the blank 8%

 

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