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 it, 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 simluation is equal to the profit from the scenario where each input assumes its expected value? Explain.

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Low-cost, high-volume sales Distribution of sales Low High Mean Value 60000 100000 Prob 0.5 0.5 Price $10 $8 Distribution of variable cost per unit Value $6.00 $7.50 $9.00 Prob 0.25 0.50 0.25 Mean Annual fixed cost $30,000 Simulation for part a Units sold Fixed cost Unit Variable cost Total Variable Cost Unit Price Total Revenue Profit Annual profit for part c, no uncertainty Mean Units Sold Fixed cost Mean Unit Variable Cost Mean Total Variable Cost Mean Unit Price Mean Revenue Mean Profit Low-cost, high-volume sales Distribution of sales Low High Mean Value 60000 100000 Prob 0.5 0.5 Price $10 $8 Distribution of variable cost per unit Value $6.00 $7.50 $9.00 Prob 0.25 0.50 0.25 Mean Annual fixed cost $30,000 Simulation for part a Units sold Fixed cost Unit Variable cost Total Variable Cost Unit Price Total Revenue Profit Annual profit for part c, no uncertainty Mean Units Sold Fixed cost Mean Unit Variable Cost Mean Total Variable Cost Mean Unit Price Mean Revenue Mean Profit