In Exercises 21–24, solve the game with the given payoff matrix, and give the expected value of the game.
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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: $ f 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) =…arrow_forwardThe 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) =…arrow_forwardThe 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. 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 1. What is Gorman's optimal decision strategy?Decision strategy:If F then .If U then . 2. What is the expected value of the market…arrow_forward
- 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 NatureLow Demand Medium Demand High DemandDecision Alternative s1 s2 s3Manufacture, d1 -20 40 100 Purchase, d2 10 45 70 The state-of-nature probabilities are 0.25, 0.35, and 0.40. Do not round your intermediate calculations. 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) = 0.90P(F|s2) = 0.40 P(U|s2) = 0.60P(F|s3) = 0.60 P(U|s3) = 0.40…arrow_forwardThe Gorman Manufacturing Company must decide whether to manufacture a component 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 S1 Medium DEmand S2 High demand S3 Manufacture, d1 -100 200 500 Purchase, d2 50 225 350 The state-of-nature probabilities are P(s1 ) = 0.35, P(s2 ) = 0.35, and P(s3) = 0.30. 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 A. What is XY Manufacturing Company optimal decision strategy? B. What is the expected value of the market…arrow_forwardThe 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 DemandS_(1) Medium DemandS_(2) High DemandS_(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. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether XY Manufacturing Company should attempt to obtain a better estimate of demand. 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?d. What…arrow_forward
- 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 DemandS_(1) Medium DemandS_(2) High DemandS_(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 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?arrow_forwardThe 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 DemandS_(1) Medium DemandS_(2) High DemandS_(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. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether XY Manufacturing Company should attempt to obtain a better estimate of demand.arrow_forward2) A payoff table is given as s1 s2 s3 d1 250 750 500 d2 300 -250 1200 d3 500 500 600 (a) If the probabilities of d1, d2, and d3 are .2, .5, and .3, respectively, then what choice should be made under expected value?arrow_forward
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