A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (i.e., there is a favorable market for the clinic), the physicians could realize a net profit of $100,000. If the market is not favorable, they could lose $40,000. Of course, they don't have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50-50 chance the clinic will be successful. Part A) Construct a decision tree to help analyze this problem. What should the medical professionals do? The physicians in case 1 have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim their experience enables them to use Bayes' theorem to make the following statements of probability: probability of a favorable market given a favorable study = 0.82 probability of an unfavorable market given a favorable study == 0.18 probability of a favorable market given an unfavorable study = 0.11 probability of an unfavorable market given an unfavorable study = 0.89 probability of a favorable research study = 0.55 probability of an unfavorable research study = 0.45