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, 0.70, and 0.10, 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		0.70	100		0.70
	High	200		0.10	300		0.10

(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?

Answer 1

for Medium-Scale Expansion :

x	f(x)	xP(x)	x2P(x)
50	0.20	10.0000	500.0000
150	0.70	105.0000	15750.0000
200	0.10	20.0000	4000.0000
	total	135.000	20250.0000
	E(x) =μ=	ΣxP(x) =	135.0000
	E(x2) =	Σx2P(x) =	20250.0000
	Var(x)=σ2 =	E(x2)-(E(x))2=	2025.0000

for Large-Scale Expansion

x	f(x)	xP(x)	x2P(x)
0	0.20	0.0000	0.0000
100	0.70	70.0000	7000.0000
300	0.10	30.0000	9000.0000
	total	100.000	16000.0000
	E(x) =μ=	ΣxP(x) =	100.0000
	E(x2) =	Σx2P(x) =	16000.0000
	Var(x)=σ2 =	E(x2)-(E(x))2=	6000.0000

a)

from above:

		EV
medium scale		135
large scale		100

medium scale decision is preferred for the objective of maximizing the expected profit

b)

		Var
medium scale		2025
large scale		6000

medium scale decision is preferred for the objective of minimizing the risk or uncertainty