   # 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 (30,000), the company can sell the product for \$20 per unit. If sales are high (70,000), a competitor will enter and the company will be able to sell the product for only \$15 per unit. The variable cost per unit has a 20% chance of being \$10, a 60% chance of being \$11, and a 20% chance of being \$12. Annual fixed costs are \$20,000. 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. ### Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

#### Solutions

Chapter
Section ### Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
Chapter 10, Problem 32P
Textbook Problem
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## 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 (30,000), the company can sell the product for \$20 per unit. If sales are high (70,000), a competitor will enter and the company will be able to sell the product for only \$15 per unit. The variable cost per unit has a 20% chance of being \$10, a 60% chance of being \$11, and a 20% chance of being \$12. Annual fixed costs are \$20,000. 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.

a)

Summary Introduction

To estimate: The expected annual profit of the firm.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

### Explanation of Solution

Formulae to determine the above table:

b)

Summary Introduction

To determine: The 95 percent interval for the annual profit of the company.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

c)

Summary Introduction

To determine: The annual profit of the firm for the given scenario.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

d)

Summary Introduction

To conclude: The results from part (a) and part (c).

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

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