(a) The maximin payoff criterion involves choosing the alternative with the highest minimum payoff. For A1, the minimum payoff is 14000, for A2 it's 19000. So, under the maximin criterion, we should choose A2. (b) The maximum likelihood criterion involves choosing the alternative with the highest payoff for the most likely state of nature. The most likely state of nature is S1 (with a probability of 0.6). The payoffs for S1 are 25000 for A1 and 23000 for A2. So, under the maximum likelihood criterion, we should choose A1. (c) The Bayes decision rule involves calculating the expected payoff for each alternative and choosing the one with the highest expected payoff. The expected payoff for A1 is (0.625000) (0.320000) (0.114000) = 22500. The expected payoff for A2 is (0.623000) (0.321000) (0.119000) = 22100. So, under the Bayes decision rule, we should choose A1