Problem $2$

Consider the following payoff table, which illustrates a capacity planning problem.

If a small facility is built, the payoff will be the same for all three possible states of

nature. For a medium facility, low demand will have a present value of $$7$ million,

whereas both moderate and high demand will have present values of $$12$ million.

A large facility will have a loss of $$4$ million if demand is low, a present value of

$$2$ million if demand is moderate, and a present value of $$16$ million if demand is

high.

POSSIBLE FUTURE DEMAND

$*$Present value in $ millions.

$($a$)$ Using the expected monetary value criterion, identify the best alternative for

the previous payoff table for these probabilities: low $=\mathrm{.}30,$ moderate $=\mathrm{.}50,$

and high $=\mathrm{.}20.$

$($b$)$ determine the expected value of perfect information.