Problem:
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?