P$2)$ A company deciding whether to launch a new product. The decision is influenced by the state of the market, which can be in one of three states: Favorable, Neutral, or Unfavorable. The company has two alternatives: to launch the product or not to launch it$.$ The payoffs and probabilities for each state of nature are as follows:

States of Nature:

$$ Favorable Market $($F$)$

$$ Neutral Market $($N$)$

$$ Unfavorable Market $($U$)$

Probabilities:

$$ P$($Favorable Market$)=0\mathrm{.}3$

$$ P$($Neutral Market$)=0\mathrm{.}5$

$$ P$($Unfavorable Market$)=0\mathrm{.}2$

Alternatives:

$$ Launch Product $($L$)$

$$ Do Not Launch Product $($D$)$

Payoffs:

$$ If the market is Favorable and the product is launched, the payoff is $$100,000.$

$$ If the market is Favorable and the product is not launched, the payoff is $$0.$

$$ If the market is Neutral and the product is launched, the payoff is $$20,000.$

$$ If the market is Neutral and the product is not launched, the payoff is $$0.$

$$ If the market is Unfavorable and the product is launched, the payoff is $-$$$50,000($a loss$).$

$$ If the market is Unfavorable and the product is not launched, the payoff is $$0.$

$1.$ Develop a Payoff table.

a$.$ What the company should do if an optimistic strategy is used $($Maximax$).$

b$.$ What the company should do if a conservative strategy is used $($Maximin$).$

c$.$ What the company should do if a minimax regret strategy is used.

d$.$ What is the expected value of the best decision if the expected value approach is used?

e$.$ What is the expected monetary value $($EMV$)$ of decision?

f$.$ What is the expected value of perfect information $($EVPI$)?$