Help me answer question $19$ and $20$

SUPPLEMENT A

DECISION MAKING

$18.$ Benjamin Moses, chief engineer of Offshore Chemicals, Inc., must decide whether to build a new processing facility based on an experimental technology. If the new facility works, the company will realize a net profit of $$20$ million. If the new facility fails, the company will lose $$10$ million. Benjamin's best guess is that there is a $40$ percent chance that the new facility will work.

What decision should Benjamin Moses make?

$19.$ 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 $$25,000$ if demand is low and earn $$140,000$ if demand is average. If demand is high, the medium$-$sized facility is expected to earn a net present value of $$150,000$; it can be expanded to a large size for a net payoff of $$145,000.$

If a large facility is built and demand is high, earnings are expected to be $$220,000.$ If demand is average for the large facility, the present value is expected to be $$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

Decision Trees

$20.$ Draw a decision tree for the three options described in problem $19.$ What should management do to achieve the highest expected payoff?

$22.$ Analyze the decision tree in the figure below. What is the expected payoff for the best alternative? First, be sure to infer the missing probabilities.Try