Chapter 3, Polynomial and Rational Functions - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 289: 64

$30x-2x^{2}$ $x=15/2$ $112.5$ sq in

(a) Cross-sectional area = $(30-2x)\times x$ $(30-2x)\times x= 30x - 2x^{2}$ (b) Maximizing$=-b\div 2a$ $a=-2,b=30$ maximum $x$ value $-30/2(-2)=15/2$ (c) maximum cross-sectional area substitute $x=15/2$ $30x-2x^{2} = 30(15/2)-2(15/2)^{2}=112.5$ sq inch