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 Reject, S₁ P(SIF) = 0.08 P(S₂IF) = 0.28 -100 100 State of Nature 1 Year, S2 50 100. 2 Years, $3 150 The probabilities for the states of nature are P(S₁) = 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. 100

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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
Produce pilot, d₁
Sell to competitor, d₂
P(F) = 0.69
P(U) =
= 0.31
P(S₁IF): = 0.08
P(S₂|F) = 0.28
P(S3|F) = 0.64
Decision Tree
Agency
No Agency
Reject, S₁
2
The probabilities for the states of nature are P(S₁) = 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(S₁U) = 0.45
P(S₂|U) = 0.39
P(S3|U) = 0.16
(a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.)
Description
3
State of Nature
4
5
1 Year, S₂
(g) What is the recommended decision?
50
100
d₁
(f) Is the agency's information worth the $5,000 fee?
Yes
No
d2
d1
Agency; if favorable, produce the pilot
Agency; if unfavorable, sell to competitor
No agency; sell to competitor
No agency; produce the pilot
d₂
What is the expected value (in thousands of dollars)?
thousand dollars
d₁
d₂
6
8
9
2 Years, S3
10
11
S₁
52
S₂
S₁
52
$3
S1
52
3
S1
S2
53
SS
S₁
5₂
S3
S₁
(b) What is the recommended decision if the agency opinion is not used?
produce pilot, d₁
sell to competitor, d₂
150
S₂
100
53
(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--- ✓
(e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.)
thousand dollars
1000⁰ 10
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 Produce pilot, d₁ Sell to competitor, d₂ P(F) = 0.69 P(U) = = 0.31 P(S₁IF): = 0.08 P(S₂|F) = 0.28 P(S3|F) = 0.64 Decision Tree Agency No Agency Reject, S₁ 2 The probabilities for the states of nature are P(S₁) = 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(S₁U) = 0.45 P(S₂|U) = 0.39 P(S3|U) = 0.16 (a) Construct a decision tree for this problem. (Enter your answers in thousands of dollars.) Description 3 State of Nature 4 5 1 Year, S₂ (g) What is the recommended decision? 50 100 d₁ (f) Is the agency's information worth the $5,000 fee? Yes No d2 d1 Agency; if favorable, produce the pilot Agency; if unfavorable, sell to competitor No agency; sell to competitor No agency; produce the pilot d₂ What is the expected value (in thousands of dollars)? thousand dollars d₁ d₂ 6 8 9 2 Years, S3 10 11 S₁ 52 S₂ S₁ 52 $3 S1 52 3 S1 S2 53 SS S₁ 5₂ S3 S₁ (b) What is the recommended decision if the agency opinion is not used? produce pilot, d₁ sell to competitor, d₂ 150 S₂ 100 53 (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--- ✓ (e) What is the expected value (in thousands of dollars) of the agency's information? (Round your answer to two decimal places.) thousand dollars 1000⁰ 10 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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