# Quanatative Methods (10 Problems) : Conservative Decisions, Events, Decision Trees, Minimax, Large and Small Demand

1. s1 s2 s3

d1 10 8 6

d2 14 15 2

d3 7 8 9

What decision should be made by the conservative decision

a. D1

b D2

c. D3

2. s1 s2 s3

d1 10 8 6

d2 14 15 2

d3 7 8 9

If the probabilities of s1, s2, and s3 are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected

a. D1

b. D2

c. D3

3. A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either small or large, with probabilities estimated to be 0.4 and 0.6 respectively. If a small plant is built, and demand is large, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be $330,000 and a 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is small, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand turns out to be small, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, when the large plant is built and the demand happens to be high, the net present value of the profits $800,000. Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the manufacturer choose?

a. Build a large plant

b. Build a small plant

c. Do not build

d. They are the same

4. Regret is the difference between the payoff from the

a. best decision and all other decision payoffs

b. best decision and the worst decision payoffs.

c. worst decision and all other decision payoffs.

d. none of the above

5. s1 s2 s3

d1 10 8 6

d2 14 15 2

d3 7 8 9

What is the EVPI?

Put your answer in the form x.x

6. The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2), or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is a 30% chance that the lot is poor quality (s1), a 50 % chance that the lot is fair quality (s2), and a 20% chance that the lot is good quality (s3).

s1 s2 s3

a1 20 30 90

a2 60 70 10

a3 80 50 40

What is the maximum amount that you would be willing to pay for perfect information?

put your answer in the form x.x or x

7. A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature

a. payoff table.

b. decision tree.

c. payback matrix.

d. feasible region.

8. People who take a chance on a bonanza with a very low probability of occurrence in lieu of a sure thing are

a. risk predictors.

b. risk takers.

c. risk calculators.

d. risk averters.

9. Which of the following is not an approach for decision making under uncertainty?

a. decision tree

b. minimax

c. maximin

d. minimax regret

10. A ________ probability is the altered marginal probability of an event based on additional information.

a. conditional

b. marginal

c. posterior

d. none of the above

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#### Solution Summary

Ten Quanatative Methods Problems involving Conservative Decisions, Events, Decision Trees, Minimax, Large and Small Demand are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.