Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Review - Modeling with Functions - Problems - Page 243: 29

Answer

(a) $L=2x+\frac{200}{x}$ (b) minimum $L=40m$ when $x=10m$ and $y=10m$

Work Step by Step

(a) Assume the length of fencing is $x$ and the width is $y$, we have $xy=100$ and $y=\frac{100}{x}$ The total length of fencing $L=2x+2y=2x+\frac{200}{x}$ (b) Graph the above function as shown in the figure. A minimum can be found $L=40m$ when $x=10m$ which gives $y=10m$
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