In Problem 19.5, you developed a payoff table for whether to purchase 100, 200, 500, or 1,000 Christmas trees. Given the results of that problem, suppose that the probabilities of the demand for the different number of trees are as follows:

Demand (Number of Trees)...................... Probability

100 ......................................................0.20

200 ......................................................0.50

500 ......................................................0.20

1,000 ....................................................0.10

a. Determine the optimal action based on the maximax criterion.

b. Determine the optimal action based on the maximin criterion.

c. Compute the expected monetary value (EMV) for purchasing 100, 200, 500, and 1,000 trees.

d. Compute the expected opportunity loss (EOL) for purchasing 100, 200, 500, and 1,000 trees.

e. Explain the meaning of the expected value of perfect information (EVPI) in this problem.

f. Based on the results of (c) or (d), would you choose to purchase 100, 200, 500, or 1,000 trees? Why?

g. Compute the coefficient of variation for purchasing 100, 200, 500, and 1,000 trees.

h. Compute the return-to-risk ratio (RTRR) for purchasing 100, 200, 500, and 1,000 trees.

i. Based on (g) and (h), would you choose to purchase 100, 200, 500, or 1,000 trees? Why?

j. Compare the results of (f) and (i) and explain any differences.

k. Suppose that the probabilities of demand are 0.4, 0.2, 0.2, and 0.2, respectively. Repeat (c) through (j) with these probabilities and compare the results with those in (c)-(j).