A business tycoon has acquired a textile company and is contemplating the future of one of its major plants, located in South Carolina. Three alternative decisions are being considered: (1) expand the plant and produce lightweight, durable materials for possible sales to the military, a market with little foreign competition; (2) maintain the status quo at the plant, continuing production of textile goods that are subject to heavy foreign competition; or (3) sell the plant now. If one of the first two alternatives is chosen, the plant will still be sold at the end of a year. The amount of profit that could be earned by selling the plant in a year depends on foreign market conditions, including the status of a trade embargo bill in Congress. The following payoff table describes this decision situation: Decision States of Nature Good foreign competitive conditions 800,000 Maintain status quo 1,300,000 320,000 Poor foreign competitive conditions 500,000 Expand Sell now -150,000 320,000 A. Determine the best decision by using the following decision criteria: 1. Maximax 2. Maximin 3. Minimax regret 4. Hurwicz (a= 30%) 5. LaPlace B. Assume that it is now possible to estimate a probability of .70 that good foreign competitive conditions will exist and a probability of .30 that poor conditions will exist. Determine the best decision by using expected value and expected opportunity loss. C. Compute the expected value of perfect information. D. Develop a decision tree, with expected values at the probability nodes. E. The business tycoon has hired a consulting firm to provide a report on future political and market situations. The report will be positive or negative, indicating either a good or poor future foreign competitive situation. The conditional probability of each report outcome, given each state of nature, is P (positive good) = 70% P (negative good) = 30% P (positive poor) = 20% P (negative poor) = 80% Determine the posterior probabilities by using Bayes' rule. F. Perform a decision tree analysis by using the posterior probability obtained in E.