Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 253: 65

Answer

(a) $-3000x^2+57000x$ (b) $9.5$ dollars (c) $19$ dollars

Work Step by Step

(a) We can model the number of attendance (y) as linearly related to the ticket price (x). When $x=10, y=27000$, and $x=9, y=27000+3000=30000$ The line equation is $\frac{y-27000}{x-10}=\frac{30000-27000}{9-10}$ $y=-3000x+57000$ The revenue is given by $R=xy=-3000x^2+57000x$ (b) The maximum of $R$ happens when $x=57000/6000=9.5$ dollars (c) Let $y=0$, we get $x=57000/3000=19$ dollars
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