Answer
(a) $V=x(600-x^2)$
(b) see graph.
(c) $x=11.1in,y=42.7in$
Work Step by Step
The total area of the four plastic sides is to be 1200 in2.
(a) Express the volume V of the shelter as a function of the depth x.
Total area $A=2x^2+2xy=1200, y=\frac{600-x^2}{x}$
Volume $V=x^2y=x(600-x^2)$
(b) Draw a graph of V.
see graph.
(c) What dimensions will maximize the volume of the shelter?
Maximum of V happens at $x=11.14in,y=42.72in$
