The athletic department at North-eastern University is considering holding an extensive campaign next year to raise funds for a new athletic field. The response to the campaign depends heavily on the success of the football team this fall. In the past, the football team has had winning seasons 60 percent of the time. If the football team has a winning season this fall, then alumni will contribute $3 million dollars. If the team has a losing season, then few will contribute and the campaign will lose $2 million. If no campaign is undertaken, no costs are incurred. On September 1, just before the season begins, the department must make a decision about the campaign. a. Develop the decision analysis formulation for this problem by identifying the decision alternatives, the states of nature, and the payoff table. b. According to Bayes’ decision rule, which decision should be undertaken? c. What is the EVPI? d. A famous football alumni has offered his services to help evaluate whether the team will have a winning season or not. For $100,000, he will carefully evaluate the team through spring practice and then through preseason workouts. He will then provide a prediction on the season. In similar situations in the past when evaluating teams that have winning seasons 60 percent of the time, his predictions have been right 75 percent of the time. If a winning season is predicted, what is the posterior probability that one will actually occur. If a losing season is predicted, what is the probability that a winning season will occur? A losing season? e. Draw the decision tree for this problem using Microsoft Powerpoint and determine the optimal policy.