1. 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 5050 chance the clinic will be successful. Construct a decision tree to help analyze this problem. What should the medical professionals do? 2. An art dealer's client is willing to buy the painting Sunplant at $50,000. The dealer can buy the painting today for $40,000 or can wait a day and buy the painting tomorrow (if it has not been sold) for $30.000. The dealer may also wait for another day and buy the painting (if it is still available) for $26,000. At the end of the third day, the painting will no longer available for sale. Each day, there is a 0.60 probability that the painting will be sold. What strategy maximizes the dealer's expected profit? 3. A company has to decide whether to invest money in the development of a microbiological product. The company's research director has estimated that there is a 60% chance that a successful development could be achieved in two years. However, if then product had not been successfully developed at the end of this period, the company would abandon the project, which would lead to a loss in present value of $3 million. In the event of a successful development a decision would have to be made on then scale of production. The returns generated would depend on the level of sales, which could be achieved over the period of the product's life. For simplicity, these have been categorized as either high or low. If the company opted for large-volume production and high sales were achieved then net returns with a present value of $6 million would be obtained. However, large-scale production followed by low sales would lead to net returns with a present value of only $1 million. On the other hand, if the company decided to invest only in small-scale production facilities then high sales would generate net returns with a present value of $4 million and low sales would generate net returns with a present value of $2 million. The company's marketing manager estimates that there is a 75% chance that high sales could be achieved. (a) Construct a decision tree to represent the company's decision problem. (b) Assuming that the company's objective is to maximize its expected returns, determine the policy that it should adopt