Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.1 Algebraic Expressions and Formulas - Exercise Set 6.1: 93

Answer

a. When x = 100, the average cost per clock is 50 dollars and 50 cents. When x = 1000, the average cost per clock is 5 dollars and 50 cents. When x = 10,000, the average cost per clock is 1 dollar. b. This business doesn't have a future if it can only produce 2000 clocks per weekly.

Work Step by Step

Part A The average cost per clock is $\frac{0.5x + 5000}{x}$ If x = 100 clocks produced, then the average cost per clock is $\frac{(0.5)(100) + 5000}{100}$ = $\frac{50 + 5000}{100}$ = $\frac{5050}{100}$ = 50.50 (50 dollars and 50 cents). If x = 1000 clocks, the average cost per clock is $\frac{(0.5)(1000) + 5000}{1000}$. This gives us $\frac{500 + 5000}{1000}$ = $\frac{5500}{1000}$ = 5.50 (5 dollars and 50 cents). If x = 10000 clocks, the average cost per clock is $\frac{(0.5)(10000) + 5000}{10000}$. This gives us $\frac{5000 + 5000}{10000}$ = $\frac{10000}{10000}$ = 1.00 (1 dollar). Part B If the company can produce 2000 clocks per week, the average cost per clock is $\frac{(0.5)(2000) + 5000}{2000}$ = $\frac{1000 + 5000}{2000}$ = $\frac{6000}{2000}$ = 3.00 (3 dollars). If the company must sell them for 50 cents more than the cost of making them (in order to make a profit(, this means they must sell each clock of 3.50 (3 dollars and 50 cents). They have a competitor that sells the clock of 1.50 (1 dollar 50 cents). This is 2 dollars below the company we are looking at, so only making 2000 clocks per week will not be profitable. Therefore the business doesn't have a future.
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