Problem 4-25 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 $1 $2 53 Manufacture, di Purchase, dz -20 40 10 45 100 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(53) 0.30. a. Use a decision tree to recommend a decision. Recommended decision: manufacture component or purchase component b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. yes or no EVPI: $ 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 $2)=0.40 P(F3)=0.60 P(US1)=0.90 P(U $2)=0.60 P(U | $3) 0.40 What is the probability that the market research report will be favorable? required, round your answer three decimal places. P(F)= d. What is Gorman's optimal decision strategy? Decision strategy: If F then If U then d1 or d2 d1 or d2 e. What is the expected value of the market research information? Expected value: $ f. What is the efficiency of the information? If required, round your answer to one decimal place. Efficiency: Problem 4-19 Hale's TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network's decision transfer the rights for the pilot and series to a competitor for $100,000. Hale's decision alternatives and profits (in thousands dollars) are as follows: State of Nature Decision Reject 1 Year, Alternative Produce pilot, di S1 -100 Sz 50 Years, S3 Sell to competitor, 100 100 100 The probabilities for the states of nature are P(S1) = 0.20, P(S2) = 0.30, and P(S3)=0.50. For a consulting fee of $5,000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant: P(F) = 0.69 P(U)=0.31 P(S1|F) = 0.09 P(S21F)=0.26 P(S3F)=0.65 a. Choose the correct decision tree for this problem. Graph a 3 -100 Favorable 50 150 100 Unfavorable 100 5, 100 Graph b Graph c P(S1U)=0.45 P(S2U) = 0.39 P(S3|U) = 0.16 -100 d 100 4 50 Agency 4 d Agency No Agency Graph d (0) Favorable (2) Unfavorable 1.50 5 100 -100 150 3 100 100 100 -100 150 4 100 100 100 -100 150 5 100 100 100 -100 d (4) 50 150 Agency Favorable d No Agency 3 Unfavorable 100 100 Graph a, b, c, or d b. What is the recommended decision if the agency opinion is not used? What is the expected value? Recommended decision: Produce or Sell Expected Value: $ c. What is the expected value perfect information? EVPI: $ d. What is Hale's optimal decision strategy assuming the agency's information is used? Produce or Sell If Favorable: If Unfavorable: Produce or Sell e. What is the expected value of the agency's information? EVSI: $ f. Is the agency's information worth the $5,000 fee? What is the maximum that Hale should be willing to pay for the information? Decision: Hale should pay no more than $ g. What is the recommended decision? Yes or No Use agency; sell the pilot No agency: sell the pilot Use agency; produce the pilot No agency: produce the pilot Problem 4-09 Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company's new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The folk table shows the estimated quarterly profits (in thousands of dollars): Demand for Service Service Strong Weak Full price $960 -$490 Discount $670 $320 a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? The input in the box below will not be graded, but may be reviewed and considered by your instructor. How many decision alternatives are there? Number of decision alternatives = How many outcomes are there for the chance event? Number of outcomes = b. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Optimistic approach Conservative approach Minimax regret approach Full price service or Discount service Full price service or Dicount service Full price service or Discount service c. Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach determine an optimal decision. Optimal Decision: Full price service or Discount service d. Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach? Optimal Decision: Full price service or Discount service e. Use graphical sensitivity analysis to determine the range of demand probabilities for which each of the decision alternatives has the largest expected value. If required, round your answer to four decimal places. if probability of strong demand is less than or equal to Full price service or Discount service Problem 4-03 Southland Corporation's decision to produce a new line of recreational products resulted in the need to construct either a small plant or a large plant. The best selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing management has decided to view the possible long-run demand as low, medium, or high. The following payoff table shows the projected profit millions of dollars: Long-Run Demand Plant Size Low Medium High Small 150 200 200 Large 50 200 500 a. What is the decision to be made, and what is the chance event for Southland's problem? The input in the box below will not be graded, but may be reviewed and considered by your instructor. b. Choose the correct influence diagram. (i) Market Demand Plant Size Profit Market Demand Plant Size Profit (iii) (iv) Plant Plant Market Profit Size Size Demand Profit tree i, ii, iii, or iv c. Choose the correct decision tree. (i) Low (iii) Small (ii) 150 Market Demand Low 150 Lage 50 50 Small Small Medium. 200 200 Medium Medium 200 Large 200 Lage High 200 Small 200 High Large 500 High 500 Medium 200 150 Small Low (iv) Low 150 Small Medium 200 High 200 Low 50 Large Medium 200 Lange High 500 tree i, ii, iii, or iv 50 Low d. Recommend a decision based on the use of the optimistic, conservative, and minimax regret approaches. Optimistic approach Conservative approach Minimax regret approach Problem 4-01 small plant or large small plant or large small plant or large High 200 Medium 200 High 500 The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision S S S3 Alternative di 250 25 dz 100 100 75 a. Choose the correct decision tree for this problem. (i) (ii) 250 S dz 100 a ch 100 (!!!) 100 250 100 $3 25 100 100 25 53 75 75 $1 (iv) 250 250 100 S 100 S $2 100 d 53 d 25 75 tree i, ii, iii, or iv 100 Sy 25 100 53 75 b. If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Optimistic approach Conservative approach Maximum regret approach d1 or d2 d1 or d2 d1 or d2