1. The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:

State of Nature

Decision Alternative    S1       S2     S3

          D1                 250      100    25

          D2                 100       100    75

A. Construct a decision tree for this problem.

B. If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative and minimax regret approaches?

2. Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table:

State of Nature

Decision Alternative     S1        S2      S3       S4

          D1                   14        9       10        5
          D2                   11        10       8        7
          D3                    9         10      10      11
          D4                    8         10      11      13

A. If the decision maker knows nothing about the probabilities of the four states of nature, what is recommended decision using the optimistic, conservative and minimax regret approaches?

B. Which approach do you prefer? Explain. Is establishing the most appropriate approach before analyzing the problem important for the decision maker? Explain.

C. Assume that the payoff table provides cost rather than profit payoffs. What is the recommended decision using the optimistic, conservative and minimax regret approaches?