Mr. and Mrs. Smith's have enjoyed sailing small boats since they were 7 years old. They want to start a company to produce small sailboats. Because fo the expense involved, they decided to conduct a pilot study. They estimate that the study will cost $10,000. Furthermore, the study can be either successful or not successful. Their decision is to build a large plant, small plant or no plant at all. With a favorable market, they can expect to make $90,000 from the large plant or $60,000 from the small plant. If the market is unfavorable, they estimate that they can lose $30,000 from a large plant or $20,000 from a small plant. They estimate that the probability of a favorable market given a successful study is 0.8. The probability of an unfavorable market given an unsuccessful study is estimated to be 0.9. They feel that there is a 50-50 chance that the study will be successful. Of course, they can bypass the study and make the decision as to whether to build a large plant, small plant, or no plant at all. Without doing any testing in a study, they estimate that the probability of a successful market is 0.6. What do you recommend?
Please look at the decision tree in the attachment (Made using Precision Tree software). As you can see that the expected value is the highest if you decide not to perform the study. The expected value in that case is 42000.
So you should not ...
The solution presents a decision tree (made in Excel) for the proposed question.