Practical Management Science
6th Edition
ISBN: 9781337671989
Author: WINSTON
Publisher: Cengage
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Chapter 9.2, Problem 1P
a)
Summary Introduction
To determine: The worst possible outcome for each decision.
Introduction: The variation between the present value of the
b)
Summary Introduction
To determine: The best possible outcome for each decision.
Introduction: The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).
c)
Summary Introduction
To determine: The variance of the distribution of the outcomes.
Introduction: The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).
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Solve the following problems using the Decision Analysis. Construct first the decision tree, and then
use Bayes' Formula to determine the optimal decision.
Decision Problems
1. The Quano Company is considering the purchase of mineral rights on a piece of property
for P1 million. The price includes a seismic test whether the land is of type X or Y
geological formation. The test cannot be done until after the purchase is made.
According to reliable information 60% of the land is of type X formation and 40% of the
area is of type Y. If the company decides to drill on the land, it will cost P2.5 million. It
may hit oil, gas, or a dry well. Drilling experience indicates that the probability of hitting
oil is 25% on X formation and 10% on Y formation. The probability of hitting gas is 30%
on X formation and 45% on Y formation. The estimated return for an oil well is P5
million and from a gas well, P3 million. Should the company purchase mineral rights?
The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:
State of Nature
Decision Alternative S1
S2
S3
di
150
100 25
d2
100
100
75
(a) Choose the correct decision tree for this problem.
(i)
(ii)
S1
150
150
$2
2
100
di
$3
100
25
83
d2
25
100
d2
$2
3
3
100
$3
S3
75
75
(iii)
S1
(iv)
150
150
2
2
d2
100
100
100
100
S2
3
3
$2
100
100
d2
$3
di
25
25
$3
4
S3
75
75
|- Select your answer - v
(b) If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?
Optimistic approach
Select your answer - v
Conservative approach
Select your answer - V
Minimax regret approach
- Select your answer
If you want to invest in a project that cost $3.5 million. As we are unsure about the future demand, there is a 40% probability of high demand with a present value for the project $3 million. There is a 25% probability of moderate demand with a present value of $2.5 million. In addition, there is a 35% probability of low demand with a present value is $1.5 million.
Draw a decision tree for this problem. What is the expected net present value of the business? Should you invest? Explain.
Assume that you can expand the project by investing another $0.6 million after you learn the true future demand state. This would make the present value of the business $3.9 million in the high‐demand state, $3.5 million in the moderate demand state, and $1.80 million in the low demand state. Draw a decision tree to reflect the option to expand. Evaluate the alternatives. What is the net present value of the business if you consider the option to expand? How valuable is the option to expand?
Chapter 9 Solutions
Practical Management Science
Ch. 9.2 - Prob. 1PCh. 9.2 - Prob. 2PCh. 9.2 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.4 - Explain in some detail how the PrecisionTree...Ch. 9.4 - Prob. 9PCh. 9.4 - Prob. 10P
Ch. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 21PCh. 9.5 - The model in Example 9.3 has only two market...Ch. 9.6 - Prob. 26PCh. 9.6 - Prob. 27PCh. 9.6 - Prob. 28PCh. 9 - Prob. 30PCh. 9 - Prob. 31PCh. 9 - Prob. 32PCh. 9 - Prob. 34PCh. 9 - Prob. 36PCh. 9 - Prob. 37PCh. 9 - Prob. 38PCh. 9 - Prob. 39PCh. 9 - Prob. 46PCh. 9 - Prob. 48PCh. 9 - Prob. 53PCh. 9 - Prob. 67PCh. 9 - Prob. 68PCh. 9 - Prob. 69PCh. 9 - Prob. 70PCh. 9 - Prob. 71PCh. 9 - Prob. 72PCh. 9 - Prob. 73PCh. 9 - Prob. 74PCh. 9 - Prob. 75PCh. 9 - Prob. 76PCh. 9 - Prob. 77P
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