A 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). Decision Alternative Low Demand $1 State of Nature -5 P(U\S₁) = 0.90 P(U|S₂) = 0.60 P(U\S3) = 0.40 Manufacture, d₁ Purchase, d₂ The state-of-nature probabilities are P(S₁) = 0.35, P(S₂) = 0.35, and P(S3) = 0.30. (a) Use a decision tree to recommend a decision. The best decision is to ---Select--the component part. 25 Medium Demand $2 55 High Demand $3 60 115 85 (b) Use EVPI to determine whether the company should attempt to obtain a better estimate of demand, assuming the estimate would come at no further cost. EVPI = The EVPI suggests that the company ---Select--- consider an 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(FIS₁) = 0.10 P(FIS₂) = 0.40 P(F|S3) = 0.60 What is the probability that the market research report will be favorable? P(F) =
A 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). Decision Alternative Low Demand $1 State of Nature -5 P(U\S₁) = 0.90 P(U|S₂) = 0.60 P(U\S3) = 0.40 Manufacture, d₁ Purchase, d₂ The state-of-nature probabilities are P(S₁) = 0.35, P(S₂) = 0.35, and P(S3) = 0.30. (a) Use a decision tree to recommend a decision. The best decision is to ---Select--the component part. 25 Medium Demand $2 55 High Demand $3 60 115 85 (b) Use EVPI to determine whether the company should attempt to obtain a better estimate of demand, assuming the estimate would come at no further cost. EVPI = The EVPI suggests that the company ---Select--- consider an 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(FIS₁) = 0.10 P(FIS₂) = 0.40 P(F|S3) = 0.60 What is the probability that the market research report will be favorable? P(F) =
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:A 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).
Decision
Alternative
Low
Demand
S1
State of Nature
-5
P(U\S₁)
= 0.90
P(U|S₂) = 0.60
P(U|s3) = 0.40
Manufacture, d₁
Purchase, d₂
The state-of-nature probabilities are P(s₁) = 0.35, P(s₂) = 0.35, and P(s3) = 0.30.
(a) Use a decision tree to recommend a decision.
The best decision is to ---Select---
25
Medium
Demand
$2
55
High
Demand
$3
60
115
85
the component part.
(b) Use EVPI to determine whether the company should attempt to obtain a better estimate of demand, assuming the estimate would come at no further cost.
EVPI =
The EVPI suggests that the company ---Select--- consider an 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|s₁) = 0.10
P(F|s₂) = 0.40
P(F|s3) = 0.60
What is the probability that the market research report will be favorable?
P(F) =
Transcribed Image Text:(d) What is the company's optimal decision strategy?
If F, then d₁. If U, then d₁.
If F, then d₂. If U, then d₁.
If F, then d₂. If U, then d₂.
If F, then d₁. If U, then d₂.
(e) What is the expected value (in thousands of dollars) of the market research information?
EVSI =
thousand dollars
(f) What is the efficiency (as a %) of the information? (Round your answer to one decimal place.)
Efficiency
%
=
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