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 0.20, 0.40, and 0.40, 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		0.20	0		0.20
	Medium	150		0.40	100		0.40
	High	200		0.40	300		0.40

(a)

Compute the expected value for the profit associated with the two expansion alternatives. Round your answers to whole numbers, if needed.

	EV
Medium-Scale
Large-Scale

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

- Select your answer -Medium-Scale Large-Scale

(b)

Compute the variance for the profit associated with the two expansion alternatives. Round your answers to whole numbers, if needed.

	Var
Medium-Scale
Large-Scale

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

- Select your answer -Medium-Scale Large-Scale

Answer 1

(a)

Medium-scale:				Large-scale:
x	P(x)	x P(x)		x	P(x)	x P(x)
50	0.2	10		0	0.2	0
150	0.4	60		100	0.4	40
200	0.4	80		300	0.4	120
Expected value = ∑x P(x) = 150				Expected value = ∑x P(x) = 160

160 > 150

Decision: Large-scale expansion

(b)

Medium-scale:						Large-scale:
x	P(x)	x P(x)	x^2 P(x)			x	P(x)	x P(x)	x^2 P(x)
50	0.2	10	500			0	0.2	0	0
150	0.4	60	9000			100	0.4	40	4000
200	0.4	80	16000			300	0.4	120	36000
Expected value = ∑x P(x) = 150						Expected value = ∑x P(x) = 160
Variance = ∑x^2 P(x) - [∑x P(x)]^2 =				3000		Variance = ∑x^2 P(x) - [∑x P(x)]^2 =				14400

3000 < 14400

Decision: Medium-scale expansion