Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.4 Solve ax(squared) + bx + c = 0 by Factoring - 4.4 Exercises - Quiz for Lessons 4-1-4.4 - Page 265: 13


See below.

Work Step by Step

Let $x$ be each $ \$10 $ decrease in price. The revenue can be modeled by the function: $R(x)=(140-10x)(50+5x)=7000+200x-50x^2$. Let's compare $R(x)$ to $f(x)=ax^2+bx+c$. We can see that a=-50, b=200, c=7000. $a\lt0$, hence the graph opens down, and its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{200}{2\cdot(-50)}=2.$ Hence the maximum value is $R(2)=-50(2)^2+200(2)+7000=7200.$ Thus they should charge $120$.
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