Solve the below problem:
Q1. 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,
Lose Contract
0.2
Bid
Do Not Bid
Win Contract
0.8
1
2
3
Market Research
No Market Research
Build Complex
Sell
6
1150
2650
650
1150
Build Complex
Sell
7
2800
800
1300
2200
0
Build Complex
Sell
5
2650
Pro t ($1000s)
Forecast High 650
0.6
Forecast Moderate
0.4
4
10
9
High Demand
0.85
Moderate Demand
0.15
High Demand
0.225
Moderate Demand
0.775
High Demand
0.6
Moderate Demand
0.4
8
DECISION TREE FOR THE DANTE DEVELOPMENT CORPORATION
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 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, s1 1 Year, s2 2 Years, s3
Produce pilot, d1 2100 50 150
Sell to competitor, d2 100 100 100
The probabilities for the states of nature are P(s1) 5 0.20, P(s2) 5 0.30, and P(s3) 5 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 following probabilities are relevant:
P(F) 5 0.69 P(s1 Z F) 5 0.09 P(s1 Z U) 5 0.45
P(U) 5 0.31 P(s2 Z F) 5 0.26 P(s2 Z U) 5 0.39
P(s3 Z F) 5 0.65 P(s3 Z U) 5 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 expected 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?
e. What is the expected value of the agency’s information?
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?
Q2. Embassy Publishing Company received a six-chapter manuscript for a new college textbook. The editor of the college division is familiar with the manuscript and estimated a 0.65 probability that the textbook will be successful. If successful, a profit of $750,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of $250,000 will occur.
Before making the decision to accept or reject the manuscript, the editor is considering sending the manuscript out for review. A review process provides either a favorable (F) or unfavorable (U) evaluation of the manuscript. Past experience with the review process suggests that probabilities P(F) 5 0.7 and P(U) 5 0.3 apply. Let s1 5 the textbook is successful, and s2 5 the textbook is unsuccessful. The editor’s initial probabilities of s1 and s2 will be revised based on whether the review is favorable or unfavorable. The revised probabilities are as follows:
P(s1 Z F) 5 0.75 P(s1 Z U) 5 0.417
P(s2 Z F) 5 0.25 P(s2 Z U) 5 0.583
a. Construct a decision tree assuming that the company will first make the decision of whether to send the manuscript out for review and then make the decision to accept or reject the manuscript.
b. Analyze the decision tree to determine the optimal decision strategy for the publishing company.
c. If the manuscript review costs $5000, what is your recommendation? Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
d. What is the expected value of perfect information? What does this EVPI suggest for the company?
Q3. Lawson’s Department Store faces a buying decision for a seasonal product for which demand can be high, medium, or low. The purchaser for Lawson’s can order one, two, or three lots of the product before the season begins but cannot reorder later. Profit projections (in thousands of dollars) are shown.
State of Nature
High Demand Medium Demand Low Demand
Decision Alternative s1 s2 s3
Order 1 lot, d1 60 60 50
Order 2 lots, d2 80 80 30
Order 3 lots, d3 100 70 10
a. If the prior probabilities for the three states of nature are 0.3, 0.3, and 0.4, respectively, what is the recommended order quantity?
b. At each preseason sales meeting, the vice president of sales provides a personal opinion regarding potential demand for this product. Because of the vice president’s Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Problems 667 enthusiasm and optimistic nature, the predictions of market conditions have always been either “excellent” (E) or “very good” (V). Probabilities are as follows:
P(E) 5 0.70 P(s1 Z E) 5 0.34 P(s1 Z V) 5 0.20
P(V) 5 0.30 P(s2 Z E) 5 0.32 P(s2 Z V) 5 0.26
P(s3 Z E) 5 0.34 P(s3 Z V) 5 0.54
What is the optimal decision strategy?
c. Use the efficiency of sample information and discuss whether the firm should consider a consulting expert who could provide independent forecasts of market conditions for the product.