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 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: State of Nature Decision Alternative Reject, $1 1 Year, $2 2 Years, $3 Produce pilot, d₁ -100 50 150 Sell to competitor, d₂ 100 100 100 The probabilities for the states of nature are P(s₁) = 0.20, P(S₂) = 0.30, and P(53) = 0.50. For a consulting fee of $5000, 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 fol- lowing probabilities are relevant: P(S₁F) = 0.09 P(S1U) = 0.45 P(F) = 0.69 P(U) = 0.31 P(S2|F) = 0.26 P($2| U) = 0.39 P(S3F) = 0.65 P(S3 | U)= 0.16 a. Construct a decision tree for this problem. b. What is the recommended decision if the agency opinion is not used? What is the ex- pected value? c. What is the expected value of perfect information? d. What is Hale's optimal decision strategy assuming the agency's information is used? What is the expected value of the agency's information? e. f. Is the agency's information worth the $5000 fee? What is the maximum that Hale should be willing to pay for the information? g. What is the recommended decision?
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 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: State of Nature Decision Alternative Reject, $1 1 Year, $2 2 Years, $3 Produce pilot, d₁ -100 50 150 Sell to competitor, d₂ 100 100 100 The probabilities for the states of nature are P(s₁) = 0.20, P(S₂) = 0.30, and P(53) = 0.50. For a consulting fee of $5000, 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 fol- lowing probabilities are relevant: P(S₁F) = 0.09 P(S1U) = 0.45 P(F) = 0.69 P(U) = 0.31 P(S2|F) = 0.26 P($2| U) = 0.39 P(S3F) = 0.65 P(S3 | U)= 0.16 a. Construct a decision tree for this problem. b. What is the recommended decision if the agency opinion is not used? What is the ex- pected value? c. What is the expected value of perfect information? d. What is Hale's optimal decision strategy assuming the agency's information is used? What is the expected value of the agency's information? e. f. Is the agency's information worth the $5000 fee? What is the maximum that Hale should be willing to pay for the information? g. What is the recommended decision?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text:### Decision Making in TV Production: Analyzing a Pilot for a Comedy Series
Hale’s TV Productions is contemplating the creation of a comedy pilot with the intention of selling it to a major television network. The network's decisions include rejecting the series, purchasing the rights for one year, or purchasing the rights for two years. Hale can either produce the pilot and wait for the network's decision or sell the pilot outright to a competitor for $100,000. The potential profits (in thousands of dollars) based on different scenarios are detailed in the following table:
| Decision Alternative | State of Nature |
|---------------------------|-------------------------------|
| | Reject, \( s_1 \) | 1 Year, \( s_2 \) | 2 Years, \( s_3 \) |
| Produce pilot, \( d_1 \) | -100 | 50 | 150 |
| Sell to competitor, \( d_2 \) | 100 | 100 | 100 |
### Probabilities of States of Nature:
- \( P(s_1) = 0.20 \)
- \( P(s_2) = 0.30 \)
- \( P(s_3) = 0.50 \)
### Consulting Agency Review:
For a $5000 consulting fee, an agency can review the pilot and predict the likelihood of network acceptance. The relevant probabilities are:
- \( P(F) = 0.69 \) (Probability of a favorable review)
- \( P(U) = 0.31 \) (Probability of an unfavorable review)
- \( P(s_1 | F) = 0.09 \) (Probability of state \( s_1 \) given a favorable review)
- \( P(s_2 | F) = 0.26 \) (Probability of state \( s_2 \) given a favorable review)
- \( P(s_3 | F) = 0.65 \) (Probability of state \( s_3 \) given a favorable review)
- \( P(s_1 | U) = 0.45 \) (Probability of state \( s_1 \) given an unfavorable review)
- \( P(s_2 | U) = 0.39 \) (Probability of state \( s_2 \) given an unfavorable review)
- \( P(s_3 | U) = 0
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