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.
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 35P
Related questions
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:
What is the probability that the |
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| (d) | What is Gorman’s optimal decision strategy? Choose the correct option. | ||||||||||
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| (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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