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 companys president must determine whether to make the expansion a medium$-$ or large$-$scale project. The demand for the new product involves an uncertainty, which for planning purposes may be low de$-$ mand, medium demand, or high demand. The probability estimates for the demands are $0\mathrm{.}20,0\mathrm{.}50,$ and $0\mathrm{.}30,$ respectively. Letting x indicate the annual profit in $$1000$s$,$ the firms planners developed profit forecasts for the medium$-$ and large$-$scale expansion projects. Unit Demand Probability$3000\mathrm{.}204000\mathrm{.}305000\mathrm{.}356000\mathrm{.}15$ DemandLow Medium HighMedium$-$Scale Expansion Profitsx f$($x$)500\mathrm{.}201500\mathrm{.}502000\mathrm{.}30$Large$-$Scale Expansion Profitsy f$($y$)00\mathrm{.}201000\mathrm{.}503000\mathrm{.}30$a$.$ Compute the expected value for the profit associated with the two expansion alterna$-$ tives. Which decision is preferred for the objective 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?