Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.7 - Optimization Problems - 4.7 Exercises: 7

Answer

$x=y=25~m$

Work Step by Step

$P = 2(x+y)$ $100 = 2(x+y)$ $50 = x + y$ $50 - x = y$ $A = xy$ $A(x) = x(50 - x)$ $A(x) = 50x - x^2$ Derivative: $A'(x) = 50 - 2x$ $0 = 50 - 2x$ $2x = 50$ $x = 25$ Substitute: $50 - 25 = y$ $25 = y$ Solve for $x$: $50-x=25$ $x=25$
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