Problem $5$S$-2($Static$)$

A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm$$s capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand: P $($low$)=\mathrm{.}3$ and P $($high$)=\mathrm{.}7.$

NEXT YEAR'S

DEMAND

Alternative Low High

Do nothing $ $50*$ $ $60$

Expand $2080$

Subcontract $4070$

$*$ Profit in $ thousands.

a$-1.$ Determine the expected profit of each alternative.