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 on 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 s 1 s 2 s 3 Manufacture, d 1 -20 40 100 Purchase, d 2 10 45 70 The state-of-nature probabilities are P(s1) = 0.25, P(s2) = 0.25, and P(s3) = 0.50 (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. Enter your answer in thousands dollars. For example, an answer of $200 thousands should be entered as 200,000. Gorman attempt to obtain a better estimate of demand, as the additional information could be worth up to $ for Gorman. (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) = 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? [Hint: We can find this value by summing the joint probability values as follows: P(F) = P(F∩s1) + P(F∩s2) + P(F∩s3) = P(s1)P(F|s1) + P(s2)P(F|s2) + P(s3)P(F|s3) .] If required, round your answer to three decimal places.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

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 on 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	s ₁	s ₂	s ₃
Manufacture, d ₁	-20		40	100
Purchase, d ₂	10		45	70

The state-of-nature probabilities are P(s₁) = 0.25, P(s₂) = 0.25, and P(s₃) = 0.50

(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. Enter your answer in thousands dollars. For example, an answer of $200 thousands should be entered as 200,000.

Gorman attempt to obtain a better estimate of demand, as the additional information could be worth up to $ for Gorman.

(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) = 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? [Hint: We can find this value by summing the joint probability values as follows: P(F) = P(F∩s₁) + P(F∩s₂) + P(F∩s₃) = P(s₁)P(F|s₁) + P(s₂)P(F|s₂) + P(s₃)P(F|s₃) .] If required, round your answer to three decimal places.

(d)

What is Gorman’s optimal decision strategy? Choose the correct option.

A.	Conduct test market, and manufacture component part, regardless of the market research report
B.	Conduct test market, and purchase component part, regardless of the market research report
C.	Conduct test market, and manufacture component part if market is favorable, or purchase component part if market is unfavorable
D.	Do not conduct test market, and purchase component part
E.	Do not conduct test market, and manufacture component part

(e)

What is the expected value of the market research information? Enter your answer in thousands dollars. For example, an answer of $200 thousands should be entered as 200,000. If your answer is zero, enter “0”.

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