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 ( s 1 ) = .35, P ( s 2 ) = .35, and P ( s 3 ) = .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 | s 1 ) = .10 P ( U | s 1 ) = .90 P ( F | s 2 ) = .40 P ( U | s 2 ) = .60 P ( F | s 3 ) = .60 P ( U | s 3 ) = .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?

BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

Solutions

Chapter
Section
Chapter 21.4, Problem 17E
Textbook Problem

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) = .35, P(s2) = .35, and P(s3) = .30.

  1. a. Use a decision tree to recommend a decision.
  2. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.
  3. 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) = .10 P(U | s1) = .90
P(F | s2) = .40 P(U | s2) = .60
P(F | s3) = .60 P(U | s3) = .40

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

  1. d. What is Gorman’s optimal decision strategy?
  2. e. What is the expected value of the market research information?

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