The Boston Red Sox and the Chicago Cubs are playing in this year's World Series. Mr. Banks, owner of a large Chicago Sporting Goods Store and a huge Cubs fan, wants to produce one-of-a-kind hats that have the name and logo of the champion printed on them. These hats will be sold immediately after the conclusion of the World Series. Therefore, he must have a good idea of who is going to win the Series in order to make a profit. It will cost Mr. Champion about $15,000 to produce the hats. Without any additional information, he believes that the Cubs have a 60% chance of winning the Series. If he is correct in his prediction of the winner, he could earn S40,000 in revenue from the sales of the hats. However, if he were incorrect, he would lose the cost of printing the hats. Before producing the hats with his anticipated Series winner and team logo on them, he may decide to consult "Ms. Predictor", a prominent baseball analyst. Procuring Ms. Predictor's services would cost $1,000 for her prediction of the outcome. Assume that in similar events, this analyst picks the Cubs 70% of the time and the Red Sox 30% of the time. Furthermore, when Ms. Predictor picks the Cubs to win, there is an 80% chance that they will indeed win, when she picks the Red Sox to win, there is a 25% chance that the Cubs will win. Using the Precision Tree add-in and the shell provided in the file Problem10_19A. xls, identify the strategy that maximizes Mr. Bank's expected profit (a) (5 pts) Find the posterior probabilities that Cubs will win given the analyst's predictions (b) (15 pts) Develop the decision tree. You must indicate the cost associated with each node and the probability associated with each arc correctly (no points will be given without this) (c) (5 pts) You want to maximize the expected profit. Find the optimal decision using the decision tree developed in (b) (d) (5 pts) What is the maximum cost of the analyst's predictions that you should be willing to pay? (e) (5 pts) Calculate the value of the perfect information