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, 0.20, and 0.60, 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		0.20	100		0.20
	High	200		0.60	300		0.60

(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

Answer:-

Given That:-

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, 0.20, and 0.60, respectively.

(a) Compute the expected value for the profit associated with the two expansion alternatives.

The expected value for the profit associated with the medium scale  expansion is

= (50) (0.2) + (150) (0.2) + (200)(0.6)

= 160

Expected value for the profit associated with the large sacle expansion is

= (0)(0.2) +(100) (0.2) + (300)(0.6)

= 200

Since E(Y) > E(X)

Large scale Expansion is preferred for the objective of maximizing the expected profit.

(b) Compute the variance for the profit associated with the two expansion alternatives.

= (50)2 (0.2) + (150)2 (0.2) + (200)2 (0.6) - (160)2

= 3400

  

= 16,000

Since V(X) < V(Y)

Medium scale expansion is preferred for the objective of minimizing the risk or uncertainity.

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