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

Question

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 demand, medium demand, or high demand. The probability estimates for the demands are 0.20, 0.50, and 0.30, respectively. Letting xindicate the annual profit in $1000s, the firms planners developed profit forecasts for the medium- and large-scale expansion projects.

                   Medium-Scale                                                   Large-Scale

                   Expansion Profits                                             Expansion Profits

                   x              f(x)                                                      y                      f(y)

Low          50               0.20                                                     0                       0.20

Demand Medium        150      0.50                                         100                   0.50

High         200              0.30                                                   300                    0.30

Explanation / Answer

E(x) = summation of xiP(xi) where i is subscript which takes value for low medium and high xi is demand P(xi) probability of demand

Medium Scale
E(x) = 50 * 0.2 + 150 *0.5+ 200* 0.3
= 10+75+60
= 145
Large-scale
E(x) = 0*0.2+100*0.5+300*0.3
=0+50+90
= 140

Medium scale is preferred for the objective of maximizing the expected
profits

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