9.7.* Consider a decision analysis problem whose payoffs (in units of thousands of dollars) are given by the following payoff table. State of Nature Alternative S1 S2 A1 80 25 A2 30 50 A3 60 40 Prior probability 0.4 0.6 a. Which alternative should be chosen under the maximax criterion? b. Which alternative should be chosen under the maximin criterion? c. Which alternative should be chosen under the maximum likelihood criterion? d. Which alternative should be chosen under Bayes' decision rule? A e. Use Analytic Solver to construct and solve a decision tree for this problem. f. Expanding the spreadsheet containing this decision tree as needed, perform sensitivity analysis with the decision tree by re-solving when the prior probability of Si is 0.2 and again when it is 0.6. A g. Now perform this sensitivity analysis systematically by generating a data table that shows the best alternative (according to Bayes' decision rule) and the resulting expected payoff as the prior probability of Si increases in increments of 0.04 from 0.2 to 0.6