You are given the following payoff table (in units of thousands of Rands) for a decision Analysis Problem. Show all formulas and calculations. Alternatives State of Nature S1 S2 S3 A1 25000 20000 14000 A2 23000 21000 19000 Prior Probability 0.6 0.3 0.1 (a) Which alternative should be chosen under the maximin payoff criterion? (1) (b) Which alternative should be chosen under the maximum likelihood criterion? (1) (c) Which alternative should be chosen under Bayes decision rule? (2) (d) Using Bayes decision rule, do sensitivity analysis graphically with respect to the prior probabilities of states S1 and S2 (without changing the prior probability of state S3) to determine the crossover point where the decision shifts from one alternative to the other. Then use algebra to calculate this crossover point. (6) (e) Repeat part (d) for the prior probabilities of states S1 and S3. (6) (f) Repeat part (d) for the prior probabilities of states S2 and S3. (6) (g) If you feel that the true probabilities of the states of nature are within 10 percent of the given prior probabilities, which alternative would you choose?