Sam has the option of conducting its own marketing research survey, at a cost of $10,000. The information from this survey could help it decide whether to build a large plant, to build a small plant, or not to build at all. Sam recognizes that although such a survey will not provide it with perfect information, it may be extremely helpful. Then, Sams first decision point is whether to conduct the $10,000 market survey. If it chooses not to do the study, it can either build a large plant, a small plant, or no plant. If the decision is to build, the market will be either favorable (.50 probability) or unfavorable (also .50 probability). Sam generates a payoff of $200,000 and $100,000 for a large plant and a small plant respectively in a favorable market. In the unfavorable market, Sams loss is -$180,000 and -$20,000 for a large plant and a small plant respectively.

If the $10,000 marketing survey is performed, the survey will indicate two results (positive and negative). First, there is a 45% chance that the survey results will indicate a favorable market. 0.78 is the probability of a favorable market for the sheds given a favorable result from the market survey. Of course, you would expect to find a high probability of a favorable market given that the research indicated that the market was good. Dont forget, though: There is a chance that Sams $10,000 market survey did not result in a favorable market. In this case, there remains a 22% chance that the market will be unfavorable.

We also note that the probability is .55 that the survey results will be negative. There is a 27% chance that the market for sheds will be favorable given negative survey results. The probability is much higher, .73, that the market will actually be unfavorable given a negative survey.

1) Draw a decision tree for the following problem.