Q1. 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 (thus netting a $10,000 profit), or can wait a day and buy the painting tomorrow (if it has not been sold) for $30,000 (netting $20,000). The dealer may also wait another day and buy the painting (if it is still available) for $26,000 (netting $24,000). At the end of the third day, the painting will no longer be available for sale. Each day, there is a 0.60 probability that the painting will be sold. Use a decision tree to identify what strategy will maximize the dealer's expected profit. Be sure to completely and clearly state the dealer's optimal strategy.
Q.2 A worker in a food plant has a rash on his left arm and the company doctor is concerned that he may be suffering from Flaubert's disease. This can only occur as a result of biological contamination of the raw materials that the worker handles in his job. However, the disease is rare and has not occurred in the plant during the ten years of its operation so the doctor estimates that the probability that contamination exists in the plant to be only 2%, while there is a 98% chance that the contamination is not present. The doctor now has to advise the company's board on whether they should close the plant for two days to enable fumigation to be carried out. This would certainly eradicate any contamination, but it would cost $30,000. If the plant is not closed and contamination is present, then it is virtually certain that other workers will fall ill. This could lead to legal action, and would amount to estimated costs of $2,000,000. The doctor has another option. A test for Flaubert's disease has just been developed, but is not totally reliable. Specifically, it has only a 60% chance of giving a correct indication. The price of the test would have to be negotiated, but it is likely to be expensive.
(a) Determine the expected value of the information from the test, assuming that the food company's objective is to minimize expected costs.
(b) If the test were perfectly reliable, what would be the value of the information it yielded