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 249: 65


$x=12$ $y=6$

Work Step by Step

Quadric function in standard form: $y=a(x-h)^2+k$, in which $(h,k)$ is the vertex. And, the maximum (or the minimum) occurs at the vertex. Two positive real numbers: $x$ and $y$ $x+2y=24$ $x=24-2y$ Product: $P=xy$ $P=(24-2y)y=24y-2y^2$ $P=-2(y^2-12y)$ $P=-2[(y^2-2(6)y+6^2)-6^2]$ $P=-2(y-6)^2+72~~$ (Notice that: $a=-2$. Parabola opens downward) So the vertex $(6,72)$ is the maximum. $x=24-2(6)=12$
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