Question

The J. R. Ryland Computer Company is considering a plant expansion to 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. Demand for the new product is uncertain, which for planning purposes may be low demand, medium demand, or high demand. The probability estimates for demand are 0.30, 0.50, and 0.20, respectively. Letting x and y indicate the annual profit in thousands of dollars, the firm's planners developed the following profit forecasts for the medium- and large-scale expansion projects.

		Medium-Scale Expansion Profit		Large-Scale Expansion Profit
		x	f(x)	y	f(y)
Demand	Low	50	0.30	0	0.30
	Medium	150	0.50	100	0.50
	High	200	0.20	300	0.20

(a)

Compute the expected value (in thousands of dollars) for the profit associated with the two expansion alternatives.

Medium-Scale thousand dollarsLarge-Scale thousand dollars

Which decision is preferred for the objective of maximizing the expected profit?

The  ---Select--- Medium-Scale Large-Scale Expansion Profit forecast is preferred for the objective of maximizing the expected profit.

(b)

Compute the variance for the profit associated with the two expansion alternatives.

Medium-ScaleLarge-Scale

Which decision is preferred for the objective of minimizing risk or uncertainty?

The  ---Select--- Medium-Scale Large-Scale Expansion Profit forecast is preferred for the objective of minimizing risk or uncertainty.

Answer 1

	x	f(x)	xp	x^2p
Low	50	0.3	15	750
Medium	150	0.5	75	11250
High	200	0.2	40	8000
			130	20000

y	f(y)	yp	y^2p
0	0.3	0	0
100	0.5	50	5000
300	0.2	60	18000
		110	23000

a)

E(X) = 130

E(Y) = 110

Since 130 > 110 , medium scale expansion is preferred for the objective of maximizing the expected profit.

b)

Var(X) = E(X^2) - (E(X))^2

= 20000-130^2

= 3100

Var(Y) = 23000 -110^2

= 10900

Since 3100 < 10900 , medium scale expansion is preferred for the objective of

minimizing the risk or uncertainty.

Please rate