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Hale's Productions is considering producing a pilot for a comedy series in the hope of selling it to a major streaming service. The streaming service 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 streaming service's decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows: Decision Alternative P(F) = 0.69 P(U) = 0.31 P(S₁IF) = 0.07 P(S₂IF) = 0.29 P(S3IF) = 0.64 Reject, S₁ Produce pilot, d₁ Sell to competitor, d₂ The probabilities for the states of nature are P(S₁) = 0.1878, P(S₂) = 0.3210, and P(S3) = 0.4912. 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 streaming service 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(S₁IU) = 0.45 P(S₂IU) = 0.39 P(S₂|U)= 0.16 -100 State of Nature 100 1 Year, S2 2 Years, S3 50 100 150 100

Hale's Productions is considering producing a pilot for a comedy series in the hope of selling it to a major streaming service. The streaming service 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 streaming service's decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows: Decision Alternative P(F) = 0.69 P(U) = 0.31 P(S₁IF) = 0.07 P(S₂IF) = 0.29 P(S3IF) = 0.64 Reject, S₁ Produce pilot, d₁ Sell to competitor, d₂ The probabilities for the states of nature are P(S₁) = 0.1878, P(S₂) = 0.3210, and P(S3) = 0.4912. 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 streaming service 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(S₁IU) = 0.45 P(S₂IU) = 0.39 P(S₂|U)= 0.16 -100 State of Nature 100 1 Year, S2 2 Years, S3 50 100 150 100

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Hale's Productions is considering producing a pilot for a comedy series in the hope of selling it to a major streaming service. The streaming service 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 streaming service's decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows: Decision Alternative P(F) = 0.69 P(U) = 0.31 P(S₁IF) = = 0.07 P(S₂IF) = 0.29 P(S3IF) = 0.64 Produce pilot, d₁ Sell to competitor, d₂ The probabilities for the states of nature are P(S₁) = 0.1878, P(S₂) 0.3210, and P(S3) = 0.4912. 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 streaming service 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(S₁IU) = 0.45 P(S₂1U) = 0.39 P(S3|U) = 0.16 Agency No Agency Reject, S1 2 F -100 100 thousand dollars (a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.) S₁ $2 3 3 4 State of Nature 5 1 Year, S₂ 2 Years, S3 (g) What is the recommended decision? d₁ d₂ (f) Is the agency's information worth the $5,000 fee? Yes No d₂ What is the expected value (in thousands of dollars)? thousand dollars d₁ Agency; if favorable, produce the pilot Agency; if unfavorable, sell to competitor No agency; sell to competitor No agency; produce the pilot d₂ 50 100 6 8 9 10 = 11 $₂ S3 S₁ 52 53 S1 S2 $3 S₁ 52 $3 (b) What is the recommended decision if the agency opinion is not used? produce pilot, d₁ sell to competitor, d₂ S1 52 150 $3 (c) What is the expected value of perfect information (in thousands of dollars)? thousand dollars 100 (d) What is Hale's optimal decision strategy assuming the agency's information is used? If favorable, ---Select--- ✓ If unfavorable, ---Select--- ♥ (e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.) m What is the maximum that Hale should be willing to pay (in thousands of dollars) for the information? (Round your answer to two decimal places.) thousand dollars
Transcribed Image Text:Hale's Productions is considering producing a pilot for a comedy series in the hope of selling it to a major streaming service. The streaming service 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 streaming service's decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows: Decision Alternative P(F) = 0.69 P(U) = 0.31 P(S₁IF) = = 0.07 P(S₂IF) = 0.29 P(S3IF) = 0.64 Produce pilot, d₁ Sell to competitor, d₂ The probabilities for the states of nature are P(S₁) = 0.1878, P(S₂) 0.3210, and P(S3) = 0.4912. 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 streaming service 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(S₁IU) = 0.45 P(S₂1U) = 0.39 P(S3|U) = 0.16 Agency No Agency Reject, S1 2 F -100 100 thousand dollars (a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.) S₁ $2 3 3 4 State of Nature 5 1 Year, S₂ 2 Years, S3 (g) What is the recommended decision? d₁ d₂ (f) Is the agency's information worth the $5,000 fee? Yes No d₂ What is the expected value (in thousands of dollars)? thousand dollars d₁ Agency; if favorable, produce the pilot Agency; if unfavorable, sell to competitor No agency; sell to competitor No agency; produce the pilot d₂ 50 100 6 8 9 10 = 11 $₂ S3 S₁ 52 53 S1 S2 $3 S₁ 52 $3 (b) What is the recommended decision if the agency opinion is not used? produce pilot, d₁ sell to competitor, d₂ S1 52 150 $3 (c) What is the expected value of perfect information (in thousands of dollars)? thousand dollars 100 (d) What is Hale's optimal decision strategy assuming the agency's information is used? If favorable, ---Select--- ✓ If unfavorable, ---Select--- ♥ (e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.) m What is the maximum that Hale should be willing to pay (in thousands of dollars) for the information? (Round your answer to two decimal places.) thousand dollars
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(a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.) Decision Tree Description Agency 1 No Agency 3 5 What is the expected value (in thousands of dollars)? 100000 * thousand dollars 6 10 (b) What is the recommended decision if the agency opinion is not used? O produce pilot, d₂ Ⓒsell to competitor, d₂ $3 (f) Is the agency's information worth the $5,000 fee? O Yes Ⓒ No -105000 45000 145000 95000 95000 95000 -105000 45000 145000 95000 95000 95000 -100000 50000 150000 100000 100000 100000 (c) What is the expected value of perfect information (in thousands of dollars)? 24560 * thousand dollars (d) What is Hale's optimal decision strategy assuming the agency's information is used? If favorable, produce .If unfavorable, sell X X X X X X X X x X X X X X X X X X (e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.) 102415 X thousand dollars What is the maximum that Hale should be willing to pay (in thousands of dollars) for the information? (Round your answer to two decimal places.) 2415 * thousand dollars
Transcribed Image Text:(a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.) Decision Tree Description Agency 1 No Agency 3 5 What is the expected value (in thousands of dollars)? 100000 * thousand dollars 6 10 (b) What is the recommended decision if the agency opinion is not used? O produce pilot, d₂ Ⓒsell to competitor, d₂ $3 (f) Is the agency's information worth the $5,000 fee? O Yes Ⓒ No -105000 45000 145000 95000 95000 95000 -105000 45000 145000 95000 95000 95000 -100000 50000 150000 100000 100000 100000 (c) What is the expected value of perfect information (in thousands of dollars)? 24560 * thousand dollars (d) What is Hale's optimal decision strategy assuming the agency's information is used? If favorable, produce .If unfavorable, sell X X X X X X X X x X X X X X X X X X (e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.) 102415 X thousand dollars What is the maximum that Hale should be willing to pay (in thousands of dollars) for the information? (Round your answer to two decimal places.) 2415 * thousand dollars
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