Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 250: 71b


When $p=24~dollars$ the maximum revenue is obtained ($R=14,400~dollars$).

Work Step by Step

We need to find the vertex of $R(p)=-25p^2+1200p$ $R(p)=-25p^2+1200p~~$ ($a=-25,b=1200,c=0$) $-\frac{b}{2a}=-\frac{-1200}{2(-25)}=24$ $f(24)=-25(24)^2+1200(24)=-14400+28800=14400$ Vertex: $(-\frac{b}{2a},f(-\frac{b}{2a}))=(24,14400)$ That is, when $p=24~dollars$ the maximum revenue is obtained ($R=14,400~dollars$).
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