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# Maximin decision rule

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Although Ken Brown (discussed in problem 3-16) is the principal owner of Brown Oil, his brother Bob is credited with making the company a financial success. Bob is vice president of finance. Bob attributes his success to his pessimistic attitude about business and the oil industry. Given the information in problem 3-16, it is likely that Bob will arrive at a different decision. What decision criterion should Bob use, and what alternative will he select?

See below for the info from 3-16

Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, Ken has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced to consider purchasing some more equipment for Brown Oil because of competition. His alternatives are shown in the following table:

Equipment Favorable Market Unfavorable Market
Sub 100 300,000 (200,000)
Oiler J 250,000 (100,000)
Texan 75,000 (18,000)

For example, if Ken purchases a sub 100 and if there is a favorable market, hje will realize a profit of 300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of 200,000. But Ken has a always been a very optimistic decision maker.

https://brainmass.com/economics/competition/maximin-decision-rule-232653

#### Solution Preview

A pessimistic decision maker like Ken Brown will use the Maximin decision rule to make a conservative decision. Under this, he would be considering the worst ...

#### Solution Summary

The Maximin decision rule is contextualized.

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## If he uses the maximax criterion, which size bus will he purchase? If he uses the maximin criteria, which size bus would he purchase? If he uses Bayes' decision rule, which size bus would he purchase? What is the expected annual profit for the bus that he will decide to purchase using Bayes' decision rule?

The operations manager for a community bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in \$000) will vary depending upon whether passenger demand is low, medium, or high as follows:

Bus Low Medium High
Small 50 60 70
Medium 40 80 90
Large 20 50 120

Prior Probabilty low .3 medium .3 high .4

If he uses the maximax criterion, which size bus will he purchase?

If he uses the maximin criteria, which size bus would he purchase?

If he uses Bayes' decision rule, which size bus would he purchase?

What is the expected annual profit for the bus that he will decide to purchase using Bayes' decision rule?

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