Question

The J. R. Ryland Computer Company is considering a plant expansion thatwill enable the company to begin production of a new computer product.The company’s president must determine whether to make the expansion amedium- or large-scale project. An uncertainty is the demand for the newproduct, which for planning purposes may be low demand, medium demand,or high demand. The probability estimates for demand are .20, .50, and .30,respectively. Letting x indicate the annual profit in $1000’s, the firm’splanners have developed the following profit forecasts for the medium- andlarge-scale expansion projects.Medium-scale Large-scaleExpansion Profits Expansion ProfitsDemand x P (x) y P (y)Low 50 .20 0 .20Medium 150 .50 100 .50High 200 .30 300 .30(a) Compute the expected value for the profit associated with the two expansionalternatives. Which decision is preferred for the ob jective ofmaximizing the expected profit?(b) Compute the variance for the profit associated with the two expansionalternatives. Which decision is preferred for the objective of minimizingthe risk or uncertainty?

Answer 1

Answer:

(a) To maximize profit select the medium scale expansion profit.

(b) To minimize risk or uncertainty select the  medium scale expansion profit.

Step-by-step explanation:

The data provided is:

                           Medium Scale              Large Scale

                        Expansion Profit         Expansion Profit

                                    x      f (x)                     y      f (y)    

                Low           50     0.2                     0      0.2

Demand Medium    150    0.5                    100   0.5

                High          200   0.3                   300    0.3

(a)

The formula to compute the expected value of a probability distribution is:

$E(U) = \sum u. f(u)$

Compute the expected value of medium scale expansion profit as follows:

$E(X)=\sum x.f(x)=(50\times0.2)+(150\times0.5)+(200\times0.3)=145$

Compute the expected value of large scale expansion profit as follows:

$E(Y)=\sum y.f(y)=(0\times0.2)+(100\times0.5)+(300\times0.3)=140$

To maximize the profit implies that we need to select the plan that will earn us a higher expected profit.

The expected profit earned from the medium scale expansion profit is $145,000.

This is more than the expected profit earned from the large scale expansion profit.

Thus, to maximize profit select the medium scale expansion profit.

(b)

The formula to compute the variance of a probability distribution is:

$V(U) = \sum (u-E(u))^{2}. f(u)$

Compute the variance of medium scale expansion profit as follows:

$V(X) = \sum (x-E(X))^{2}. f(x)\\=[(50-145)^{2}\times0.2]+[(150-145)^{2}\times0.5]+[(200-145)^{2}\times0.3]\\=2725$

Compute the variance of large scale expansion profit as follows:

$V(Y) = \sum (y-E(Y))^{2}. f(y)\\=[(0-140)^{2}\times0.2]+[(100-140)^{2}\times0.5]+[(300-140)^{2}\times0.3]\\=12400$

To minimize the risk or uncertainty implies that the variance must be as small as possible.

The variance for medium scale expansion profit is less than the large scale expansion profit.

Thus, to minimize risk or uncertainty select the  medium scale expansion profit.