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, mel demand, or high demand. The probability estimates for demand are 0.20, 0.30, and 0.50, respectively. Letting x and y indicate the annual profit in thousands of dollars, the planners developed the following profit forecasts for the medium and large-scale expansion projects Medium Scale Expansion Profit Large Scale Expansion Profit f(y) SO Demand Medium 0.20 0.30 0.50 150 200 0.30 100 300 (a) Compute the expected value for the profit associated with the two expansion alternatives. Round your answers to whole numbers, I needed EV Medium-Scale Large-scale Which decision is preferred for the objective of maximizing the expected profit Select your answer (b) Compute the variance for the profit associated with the two expansion alternatives. Round your an Var Medium Scale Large-Scale Which decision is preferred for the objective of minimizing the risk or uncerta Select your answer

Answer 1

Solution: the Medium - Value for the profft associated with (a) The expected value for the profit associated with scale expansion ECX) = Exif() = (50) (0.20) + (150)(0.30) + 200(0:50) = 10+ 45+ 100 ni E(X) = 156 = 155 The expected value for the profit associated with the large-scale expansion ECY) = Ey; flyr) = (0) (0, 20) +(100) (0-30)+ (0,50X300) = 30+ 150 = 180 • Ely) = 180 Hence, myge, scale is preferred for the objective of maximi zing the expected profit. (b) The variance for the profit associated with the Medium - Scale eырамі м V(X) = ECX) - [Ecx)] = [ty f(xi) -(155)? = (2500) (0,20)+(22500 )(0.30)+(40000)(0.50) — 24025 = 500 + 6750+ 20000 – 24025 = 3225 The Variance for the profit associated with the large-scale expansion Vly) - Ely?) – (ECY)] = [ yicfig;) – (180)2 = 000.20) + 1000000. 30)+ 90000 (0.50) – 324100 = 3000 + 45000 -32400 = 15600 : Medium Scale is preferred for the objective of minimizing or uncertainty e risk.