The operations manager for a local micro$-$loan bank wants to decide what type of loan the bank will offer to the community. The estimated annual profits $($in millions$)$ depend upon whether the business economy is growing, stable, or declining as follows:

Type of Loan

Growing

Stable

Declining

Business Loan

$25$

$10$

$2\mathrm{.}5$

Micro Loan

$10$

$10$

$7\mathrm{.}5$

A$.$ Recommend a decision based on the use of

$1.$ Optimistic $($maximax$)$

$2.$ Conservative $($minimax$)$

$3.$ Minimax regret

B$.$ Suppose the decision maker obtained the probability assessments of P$($high$)=0\mathrm{.}65,$ P$($Medium$)=0\mathrm{.}15$ and P$($Low$)=0\mathrm{.}20.$ Use the expected value approach to determine the optimal

decision.

$1.$ What is the expected value with perfect information $($EVwPI$)?$