The J$.$ R$.$ Ryland Computer Company is considering a plant expansion that

will enable the company to begin production of a new computer product.

The company$$s president must determine whether to make the expansion a

medium$-$ or large$-$scale project. An uncertainty is the demand for the new

product, which for planning purposes may be low demand, medium demand,

or high demand. The probability estimates for demand are $\mathrm{.}20,\mathrm{.}50,$ and $\mathrm{.}30,$

respectively. Letting x indicate the annual profit in $$1000$s$,$ the firm$$s

planners have developed the following profit forecasts for the medium$-$ and

large$-$scale expansion projects.

Medium$-$scale Large$-$scale

Expansion Profits Expansion Profits

Demand x P $($x$)$ y P $($y$)$

Low $50\mathrm{.}200\mathrm{.}20$

Medium $150\mathrm{.}30100\mathrm{.}30$

High $200\mathrm{.}50300\mathrm{.}50$

$($a$)$ Compute the expected value for the profit associated with the two expansion

alternatives. Which decision is preferred for the ob jective of

maximizing the expected profit?

$($b$)$ Compute the variance for the profit associated with the two expansion

alternatives. Which decision is preferred for the objective of minimizing

the risk or uncertainty?