The XY Manufacturing Company must decide whether to manufacture acomponent part at its 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 ten thousand of pesos): State of NatureState of NatureState of NatureDecision AlternativeLow DemandS_(1)Medium DemandS_(2)High DemandS_(3)Manufacture, d_(1)-100200500Purchase, d_(2)50225350The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30.c. A test market study of the potential demand for the product is expected to reporteither a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:What is the probability that the market research report will be favorable? SAP(F|s₁) = 0.10P(F|$₂) = 0.40P(F|53) = 0.60P(U|s₁) = 0.90P(U|$₂) = 0.60P(U|53) = 0.40

Answered: Image /qna-images/answer/c77c4aeb-ea5e-4e36-8d3c-9e5ccd42a69b.jpg

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

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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 54CR

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Question

The XY Manufacturing Company must decide whether to manufacture acomponent part at its 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 ten thousand of pesos):

	State of Nature	State of Nature	State of Nature
Decision Alternative	Low Demand S_(1)	Medium Demand S_(2)	High Demand S_(3)
Manufacture, d_(1)	-100	200	500
Purchase, d_(2)	50	225	350

The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3
) = 0.30.

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

SA
P(F|s₁) = 0.10
P(F|$₂) = 0.40
P(F|53) = 0.60
P(U|s₁) = 0.90
P(U|$₂) = 0.60
P(U|53) = 0.40

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