Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Chapter Test - Page 188: 18

Answer

(a) $ -\frac{1}{10}x^2+1000x$ (b) $384,000\ dollars$. (c) $ 5000\ units$, $ 2,500,000\ dollars$. (d) $ 500\ dollars$.

Work Step by Step

(a) Based on the given conditions, we can find $R(x)=px=-\frac{1}{10}x^2+1000x$ (b) Let $x=400$, we have $R(400)=-\frac{1}{10}(400)^2+1000(400)=384,000\ dollars$. (c) With $a=-\frac{1}{10}, b=1000$, to maximizes revenue, we need $x=-\frac{b}{2a}=-\frac{1000}{2(-1/10)}=5000\ units$, and $R(5000)=-\frac{1}{10}(5000)^2+1000(5000)=2,500,000\ dollars$. (d) At $x=500$, we have $p(5000)=-\frac{1}{10}(5000)+1000=500\ dollars$.
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