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# Using a Decision Tree to Solve a Problem

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a) Draw a decision tree to solve Jim's problem. Explain how you have calculated all the probabilities that you report on the tree. Define clearly each decision node, event node, decision that you can take, and possible outcome for the random variables.

b) What is the best decision for Jim amongst opting for survey or pilot study or none?

c) Suppose that the cost of the pilot study can be cut down to \$15,000. Does it affect Jim's best decision?

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#### Solution Preview

Jim Sellers considers producing a new type of electric razor for men. If the market is favorable, he would get a return of \$100000, but, if the market is unfavorable, he would lose \$60000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research Company to gather additional information about the razor market. Bush has suggested that Jim either use a survey, or a pilot study to test the market. The survey is a sophisticated questionnaire administered to a test market, and costs \$5000. Another alternative is to run a pilot study. This would involve producing a limited number of new razors and trying to sell them in two representative American cities. The pilot study is more accurate but is also more expensive: it costs \$20000.

Ron Bush has proposed Jim to conduct either the survey, or the pilot study before making any decision regarding the production of the new razor. Jim is however not convinced that the contribution of the survey, or that of the pilot study, is worth its cost. Jim estimates that the unconditional probability of a successful market ...

\$2.19
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