Quantitative Methods Dm homework

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Homework Chapter 3
Clearly show your calculations in all the problems. Points will not be earned if you do not
show calculations.
1. The following is a payoff table giving profits for various situations.
Alternatives
Alternative 1
Alternative 2
Alternative 3
Do Nothing
States of Nature
A
B
140
160
220
120
120
140
0
0
C
140
70
200
0
What decision would a pessimist make?
2. The following is a payoff table giving profits for various situations.
Alternatives
Alternative 1
Alternative 2
Alternative 3
Do Nothing
States of Nature
A
B
140
160
220
120
120
140
0
0
C
140
70
200
0
What decision should be made based on the minimax regret criterion?
3. Dr. McFadden, a surgeon, must decide what mode of treatment to use on Mr.
Samuels. There are three modes of treatment: Mode A, B, and C; and three possible
states of nature: 1. Treatment succeeds, and patient leads a normal life, 2. Patient
survives treatment but is permanently disabled, and 3. Patient fails to survive
treatment. The probability of that the patient leads a normal life is 0.4, Disability is 0.4
and Non-survival is 0.2. Dr. McFadden has prepared the decision table below. What
mode of treatment maximizes the expected value?
Treatment Mode
A
B
C
P(outcome)
Outcome
Normal Life
$1,000,000
$3,000,000
$4,000,000
0.4
EMV
Disability
-$2,000,000
-$2,500,000
-$3,000,000
0.4
Non-Survival
-$500,000
-$500,000
-$600,000
0.2
4. A plant manager considers the operational cost per hour of five machine alternatives.
The cost per hour is sensitive to three potential weather conditions: cold, mild, and
warm. The following table represents the operations cost per hour for each alternativestate of nature combination:
Alternatives
Machine 1
Machine 2
Machine 3
Machine 4
Machine 5
States of Nature
Weather related cost per hour
Cold cost/day Mild cost/day Warm cost/day
$42
$40
$45
$45
$42
$47
$40
$35
$54
$60
$30
$48
$45
$40
$45
Using the optimistic criterion, which alternative is best?
5. A plant manager considers the operational cost per hour of five machine alternatives.
The cost per hour is sensitive to three potential weather conditions: cold, mild, and
warm. The following table represents the operations cost per hour for each alternativestate of nature combination:
Alternatives
Machine 1
Machine 2
Machine 3
Machine 4
Machine 5
States of Nature
Weather related cost per hour
Cold cost/day
Mild cost/day Warm cost/day
$42
$40
$45
$45
$42
$47
$40
$35
$54
$60
$30
$48
$45
$40
$45
EMV
Assume that for a randomly selected day, there is a 30% probability of cold weather,
50% probability of mild weather, and 20% probability of warm weather. What is the
EVPI?
6. Barbour Electric is considering the introduction of a new product. This product can
be produced in one of several ways: (a) using the present assembly line at a cost of $20
per unit, (b) using the current assembly line after it has been overhauled (at a cost of
$5,000) with a cost of $18 per unit; and (c) on an entirely new assembly line (costing
$20,000) designed especially for the new product with a per unit cost of $15. Barbour is
worried, however, about the impact of competition. If no competition occurs, they
expect to sell 10,000 units the first year. With competition, the number of units sold is
expected to drop to 6,000. At the moment, their best estimate is that there is a 40%
chance of competition. They have decided to make their decision based on the first year
sales.
(a) Develop a decision table (EOL).
(b) What decision should they make?

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