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, 0.50, and 0.30, 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		0.50	100		0.50
	High	200		0.30	300		0.30

(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-ScaleLarge-ScaleItem 3

(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-ScaleLarge-Scale

Answer 1

x	y	f(x,y)	x*f(x,y)	y*f(x,y)	x^2f(x,y)	y^2f(x,y)	xy*f(x,y)
50	0	0.2	10	0	500	0	0
150	100	0.5	75	50	11250	5000	7500
200	300	0.3	60	90	12000	27000	18000
	Total	1	145	140	23750	32000	25500
	E(X)=ΣxP(x,y)=					145
	E(X2)=Σx2P(x,y)=					23750
	E(Y)=ΣyP(x,y)=					140
	E(Y2)=Σy2P(x,y)=					32000
	Var(X)=E(X2)-(E(X))2=					2725.00
	Var(Y)=E(Y2)-(E(Y))2=					12400.00

a)

medium scale EV =145

large scale EV =140

Medium-Scale

b)

Medium-Scale variance =2725

large-Scale variance =12400

Medium-Scale