# The following is a payoff table giving profits for various situations

1. The following is a payoff table giving profits for various situations.

 States of Nature Alternatives A B C Alternative 1 140 160 140 Alternative 2 220 120 70 Alternative 3 120 140 200 Do Nothing 0 0 0

What decision would a pessimist make?

2.

The following is a payoff table giving profits for various situations.

 States of Nature Alternatives A B C Alternative 1 140 160 140 Alternative 2 220 120 70 Alternative 3 120 140 200 Do Nothing 0 0 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 Outcome Normal Life Disability Non-Survival A \$1,000,000 -\$2,000,000 -\$500,000 B \$3,000,000 -\$2,500,000 -\$500,000 C \$4,000,000 -\$3,000,000 -\$600,000 P(outcome) 0.4 0.4 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 alternative-state of nature combination:

 States of Nature Weather related cost per hour Alternatives Cold cost/day Mild cost/day Warm cost/day Machine 1 \$42 \$40 \$45 Machine 2 \$45 \$42 \$47 Machine 3 \$40 \$35 \$54 Machine 4 \$60 \$30 \$48 Machine 5 \$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 alternative-state of nature combination:

 Alternatives States of Nature EMV Weather related cost per hour Cold cost/day Mild cost/day Warm cost/day Machine 1 \$42 \$40 \$45 Machine 2 \$45 \$42 \$47 Machine 3 \$40 \$35 \$54 Machine 4 \$60 \$30 \$48 Machine 5 \$45 \$40 \$45 0.3 0.5 0.2

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?

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?

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