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 Produce pilot, d₁ Sell to competitor, d₂ P(F) = 0.69 P(U) = 0.31 P(S₁IF) = 0.08 P(S₂IF) = 0.28 P(S3|F) = 0.64 Decision Tree Agency 1 Reject, S1 No Agency The probabilities for the states of nature are P(s) = 0.1947, P(S₂) = 0.3141, 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. F -100 U 100 P(S₂IU) = 0.45 P(S₂IU) = 0.39 P(S3|U) = 0.16 (a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.) Description thousand dollars 3 State of Nature 4 5 1 Year, S₂ (g) What is the recommended decision? 50 100 What is the expected value (in thousands of dollars)? thousand dollars (f) Is the agency's information worth the $5,000 fee? Yes No 6 2 Years, S3 10 O Agency; if unfavorable, sell to competitor Agency; if favorable, produce the pilot O No agency; produce the pilot O No agency; sell to competitor 11 $₁ $₂ $3 $3 (b) What is the recommended decision if the agency opinion is not used? produce pilot, d₂ O sell to competitor, d₂ 150 $2 S3 100 $2 $3 (c) What is the expected value of perfect information (in thousands of dollars)? thousand dollars. (d) What is Hale's optimal decision strategy assuming the agency's information is used? If favorable, --Select-- . If unfavorable, --Select--- 0. (e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.) 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

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 Produce pilot, d₁ Sell to competitor, d₂ P(F) = 0.69 P(U) = 0.31 P(S₁IF) = 0.08 P(S₂IF) = 0.28 P(S3|F) = 0.64 Decision Tree Agency 1 Reject, S1 No Agency The probabilities for the states of nature are P(s) = 0.1947, P(S₂) = 0.3141, 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. F -100 U 100 P(S₂IU) = 0.45 P(S₂IU) = 0.39 P(S3|U) = 0.16 (a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.) Description thousand dollars 3 State of Nature 4 5 1 Year, S₂ (g) What is the recommended decision? 50 100 What is the expected value (in thousands of dollars)? thousand dollars (f) Is the agency's information worth the $5,000 fee? Yes No 6 2 Years, S3 10 O Agency; if unfavorable, sell to competitor Agency; if favorable, produce the pilot O No agency; produce the pilot O No agency; sell to competitor 11 $₁ $₂ $3 $3 (b) What is the recommended decision if the agency opinion is not used? produce pilot, d₂ O sell to competitor, d₂ 150 $2 S3 100 $2 $3 (c) What is the expected value of perfect information (in thousands of dollars)? thousand dollars. (d) What is Hale's optimal decision strategy assuming the agency's information is used? If favorable, --Select-- . If unfavorable, --Select--- 0. (e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.) 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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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