(Class 3 (a)-(d), Class 5 (e)) [30 points total] Farmer John sells fruit and vegetables at a farmer's market in the middle of a city. He is bringing tomatoes to the city for this weekend's farmer's market. The tomatoes are very ripe and, therefore, he will need to sell the tomatoes at the farmer's market and then have to discard any that were not sold. However, there is a cost to the farmer to bring tomatoes into the city for the farmer's market. In particular, it costs the farmer $1.75 per case of tomatoes to prepare them and bring them to the market. Farmer John can sell each case for \$4.5. Farmer John estimates that he will be able to sell 12 , 13,14 , or 15 cases of tomatoes at the farmer's market. Based on historical sales, he believes that the probabilities of being able to sell 12,13,14, and 15 cases are 0.1,0.3,0.4, and 0.2 , respectively. (a) (10 points) Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table. You do not need to consider 'opportunity costs' or lost sales costs in the payoff table. 1 (b) (4 points) How many cases of tomatoes will Farmer John bring if he uses the maximin payoff criteria? (c) (4 points) How many cases will he bring if he uses the maximum likelihood criteria? (d) (4 points) How many cases should be brought according to Bayes' decision rule? (e) (8 points) Determine the expected value of perfect information for this decision-making environment