A hardware company sells a lot of low-cost, highvolumeproducts. For one such product, it is equallylikely that annual unit sales will be low or high. Ifsales are low (60,000), the company can sell theproduct for $10 per unit. If sales are high (100,000),a competitor will enter and the company will be ableto sell the product for only $8 per unit. The variablecost 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 expectedannual profit.b. Find a 95% interval for the company’s annualprofit, that is, an interval such that about 95% ofthe actual profits are inside it.c. Now suppose that annual unit sales, variable cost,and unit price are equal to their respective expectedvalues—that is, there is no uncertainty. Determinethe company’s annual profit for this scenario.d. Can you conclude from the results in parts a and cthat the expected profit from a simulation is equalto the profit from the scenario where each inputassumes its expected value? Explain.
A hardware company sells a lot of low-cost, highvolume
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.
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