Question

Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes that any leftover goods will have to be scrapped. How many units should be ordered in February

Answer 1

Based on the concept of expected value, the units that the company should order to meet February demand is 57 units.

What is expected value?

In mathematics under the probability distribution theory, the expected value is the weighted average of possible values of some random variables.  The weights are based on the theoretical probabilities of the variables.

Data and Calculations:

Cost per unit = $20

Selling price per unit = $50

Projected Demand

  Demand Units    Probability      Expected Demand Units

1.    50 units             40%                 20 units (50 x 40%)

2.   60 units             50%                 30 units (60 x 50%)

3.   70 units              10%                    7 units (70 x 10%)

Total expected demand units =    57 units

Thus, the expected demand in February is 57 units.

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