You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem.

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?
e. Construct a decision tree by hand for this problem.
f. Use RSPE to construct and solve a decision tree for this problem.
g. Perform sensitivity analysis with this decision tree by generating a data table that shows what happens when the prior probability of S1 increases in increments of 0.05 from 0.3 to 0.7 while the prior probability of S3 remains fixed at its original value.
Then use trial and error to estimate the value of the prior probability of S1 at which the best alternative changes as this prior probability increases.
h. Repeat part g when it is the prior probability of S2 that remains fixed at its original value.
i. Repeat part g when it is the prior probability of S1 that remains fixed at its original value while the prior probability of S2 increases in increments of 0.05 from 0 to 0.4.
j. If you feel that the true probabilities of the states of nature should be within 10 percent of the given prior probabilities, which alternative would you choose?

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State of Nature S2 Alternative S3 A, 220 170 110 Az 200 180 150 Prior probability 0.1 0.6 0.3