Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Review Exercises - Page 249: 20

Answer

$(500,42500)$. This means that when we sold or produced $500$ calculators, both cost and revenue are $\$42,500$.

Work Step by Step

The given functions are $C(x)=22,500+40x$ and $R(x)=85x$ The break-even point is the intersection point of cost and revenue lines. At the break even point both functions are equal. $\Rightarrow R(x)=C(x)$. Substitute both values and solve for $x$. $\Rightarrow 85x=22,500+40x$ Subtract $40x$ from both sides. $\Rightarrow 85x-40x=22,500+40x-40x$ Simplify. $\Rightarrow 45x=22,500$ Divide both sides by $45$. $\Rightarrow \frac{45x}{45}=\frac{22,500}{45}$ Simplify. $\Rightarrow x=500$ Plug $x=500$ into cost function. $\Rightarrow 22,500+40(500)$. Simplify. $\Rightarrow 22,500+20000$. $\Rightarrow 42,500$. Hence, the break-even point is $(500,42500)$. This means that when we sold or produced $500$ calculators, both cost and revenue are $\$42,500$.
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