A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being $0\mathrm{.}25,0\mathrm{.}40,$ and $0\mathrm{.}35,$ respectively.

A small facility is expected to earn an after$-$tax net present value of just $$18,000$ if demand is low. If demand is average, the small facility is expected to earn $$75,000$; it can be increased to medium size to earn a net present value of $$60,000.$ If demand is high, the small facility is expected to earn $$75,000$ and can be expanded to medium size to earn $$60,000$ or to large size to earn $$125,000.$

A medium$-$sized facility is expected to lose an estimated $$20,000$ if the demand is low and earn $$140,000$ if demand is average. If demand is high, the medium$-$sized facility is expected to earn net present value of $$150,000$; it can be expanded to a large size for a net payoff of $$145,000.$

If large facility is built and demand is high, earnings are expected to be $$220,000.$ If demand is average for the large facility, the net present value is expected to be $$125,000$; if demand is low, the facility is expected to lose $$60,000.$

Which alternative is best, according to each of the following decision criterion?

a$.$ Maximin

b$.$ Maximax

c$.$ Minimax regret