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 DemandMedium DemandHigh DemandDecision Alternatives1s2s3Manufacture, d1-2040100Purchase, d2104570 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. 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 3A 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) = 0.90P(F | s2) = 0.40 P(U | s2) = 0.60P(F | s3) = 0.60 P(U | s3) = 0.40What 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 4What 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 7What 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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Answered: The Gorman Manufacturing Company must…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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.

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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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