Question

2. The L.&J. company is considering a plant to upgrade the production equipment for a new product. There are two options: a medium-scale upgrade, or a large-scale upgrade. The manager is asked to making a decision based on the following tradeoff: demand for the new product is uncertain, which could be low demand, medium demand, or high demand. The probability estimates for demand are 0.2, 0.5, 0.3, respectively. Let x and y indicate the annual profit in thousands of dollars, the manager developed the following profit forecasts for the medium- and large-scale upgrade.

Medium-scale upgrade Large-scale upgrade demand x Prob. f(x) y Prob.f(y) Low 50 0.2 0 0.2 Medium 150 0.5 100 0.5 High 200 0.3 300 0.3 1) Which decision is preferred for the objective of maximizing the expected profit?

Answer 1

Medium-scale upgrade Large-scale upgrade demand

x Prob. f(x) y Prob.f(y)

Low 50 0.2 0 0.2

Medium 150 0.5 100 0.5

High 200 0.3 300 0.3

For Medium scale upgrade, the expected annual profit is,

= 0.2 * 50 + 0.5 * 150 + 0.3 * 200 = 145 thousands of dollars

For Large scale upgrade, the expected annual profit is,

= 0.2 * 0 + 0.5 * 100 + 0.3 * 300 = 140 thousands of dollars

As, the expected annual profit for Medium scale upgrade is greater than the expected annual profit for Large scale upgrade, Medium scale upgrade is preferred for the objective of maximizing the expected profit.