College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.1 - Page 347: 100


See below.

Work Step by Step

Obviously it is worth having at least $50$ trees per acre. Then if we increase the number of trees by $x$, the function modeling the income will be: $(50+x)(320-4x)=-4x^2+120x+16000$ The maximum value is at $x=-\frac{b}{2a}=-\frac{120}{2\cdot(-4)}=15.$ Hence the maximum value is $f(15)=-4\cdot15^2+120(15)+16000=16900.$ Thus the number of trees should be $50+15=65$ and the income will be $16900$.
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