A hardware company sells a lot of low-cost, high volume products. For one such product, it is equally likely that annual unit sales will be low or high. If sales are low (60,000), the company can sell the product for $10 per unit. If sales are high (100,000), a competitor will enter and the company will be able to sell the product for only $8 per unit. The variable cost per unit has a 25% chance of being $6, a 50% chance of being $7.50, and a 25% chance of being $9. Annual fixed costs are $30,000.
a. Use simulation to estimate the company’s expected annual profit.
b. Find a 95% interval for the company’s annual profit, that is, an interval such that about 95% of the actual profits are inside it.
c. Now suppose that annual unit sales, variable cost, and unit price are equal to their respective expected values—that is, there is no uncertainty. Determine the company’s annual profit for this scenario.
d. Can you conclude from the results in parts a and c that the expected profit from a simulation is equal to the profit from the scenario where each input assumes its expected value? Explain.