$5.$ A manager is trying to decide whether to build a small, medium or large facility. Demand can be high, average, or low, with the estimated probabilities being $0\mathrm{.}15,0\mathrm{.}50,$ and $0\mathrm{.}35,$ respectively. The following payoff table has been created to help with the decision:

Decision High Demand Average Demand Low Demand

Small Facility $$80,000$ $$90,000$ $$100,000$

Med Facility $$115,000$ $$150,000$ $$35,000$

Large Facility $$185,000$ $$95,000$ $$15,000$

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

a$.$ Maximin

b$.$ Maximax

c$.$ Laplace

d$.$ Minimax regret

e$.$ Expected value