I dont need the decesion tree part. Can you answer the rest? Problem 13-19 (Algo
ID: 431637 • Letter: I
Question
I dont need the decesion tree part. Can you answer the rest?
Problem 13-19 (Algorithmic)
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 $200,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows:
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 $25,000, 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:
Choose the correct decision tree for this problem.
What is the recommended decision if the agency opinion is not used? What is the expected value? Enter your answer in thousands of dollars.
Recommended decision
Expected Value = $ thousands.
What is the expected value of perfect information? Enter your answer in thousands of dollars.
EVPI = $ thousands.
What is Hale's optimal decision strategy assuming the agency's information is used?
If Favorable
If Unfavorable
What is the expected value of the agency's information? Round your answer to two decimal places. Enter your answer in thousands of dollars.
EVSI = $ thousands.
Is the agency's information worth the $25,000 fee? What is the maximum that Hale should be willing to pay for the information?
Decision
Hale should pay no more than $ thousands. Round your answer to two decimal places. Enter your answer in thousands of dollars.
What is the recommended decision?
Explanation / Answer
Premise
There are two alternative decisions. Produce pilot (d1) and sell to competitor (d2)
There are three states of nature and their probabilities Reject (s1), 1 Year (s2) and 2 Years (s3) with probabilities of 0.2, 0.3 and 0.5 respectively.
Agency review may be favorable or unfavorable with a probability of 0.68 and 0.32 respectively. The probabilities of states of nature will be further refined to P(s1|F) = 0.07, P(s2|F) =0.23, and P(s3|F) = 0.70 in case of favorable. Otherwise it will be P(s1|U) = 0.42, P(s2|U) = 0.33, and P(s3|U) = 0.25
In order to calculate the expected value of decisions we need to multiply the probabilities and the results of the decision. Then compare them to choose the higher valued item. Using this we have
Produce pilot = -150*0.2 + 150*0.3 + 450*0.5 = 240
Sell to competitor = 200*0.2 + 200* 0.3 + 200 *0.5 = 200
The decision will be to produce the pilot and the expected value is 240 (EV)
The expected value of perfect information is the difference between the expected value with perfect information and the expected value without perfect information. This means
EVPI = EVwPI = EV
EVwPI is given by the best value for each state of nature. Thus EVwPI is
200*0.2 + 200*0.3 + 450*0.5 =325
Now we have the EV as 240 and that makes the EVPI as 325-240 = 85 (EVPI)
Now if we hire the consultant, and the consultant gives a favorable verdict then the expected value of the favorable decisions are
Produce pilot = -150*0.07 + 150*0.23 + 450*0.70 = 339
Sell to competitor = 200*0.07 + 200* 0.23 + 200 *0.70 = 200
The EV for favorable decision is 339 (EV|F)
If the decision of the consultant is unfavorable then we have
Produce pilot = -150*0.42 + 150*0.33 + 450*0.25 = 99
Sell to competitor = 200*0.42 + 200* 0.33 + 200 *0.25 = 200
The EV for unfavorable decision is 200 (EV|U)
The EV of hiring the consultant is 339*0.68 + 200*0.32 = 294.52
From the previous problem we know that EV of not using the consultant is 240. EVSI is given by EVwSI (this the EV using the consultant) – EV
EVSI = 294.52-240 = 54.52
Since the values are in thousands, the value of consultant’s sample information is worth $54520. Hale should be willing to pay for the information.
Recommended decision will be to pay the consultant.
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