7. (a) A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm's capacity. The contractor must now make a decision on the capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Which alternative should be selected if the decision criterion is: i. Maximax? ii. Maximin? iii. Laplace? iv. Minimax regret? (b) Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand: P( low )=.3 and P( high )=.7. i. Determine the expected profit of each alternative. Which alternative is best? Why? ii. Analyze the problem using a decision tree. Show the expected profit of each alternative on the tree. iii. Compute the expected value of perfect information