Assignment:
Q1. 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?
Q2. 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?
Provide complete and step by step solution for the question and show calculations and use formulas.