Math

StatisticsSTATISTICS F/BUSINESS+ECONOMICS-TEXTThe 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*launch*

13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

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*(*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?

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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