Question

A rancher wishes to enclose a rectangular pasture with 320 feet of fencing. the fencing will be used on three sides of the pasture, and the fourth side of the pasture will be bounded by a wall. what dimensions should the pasture have in order to maximize its area?

Answer 1

Let each side perpendicular to the wall be x
The parallel to the wall will be 320-2x
the area will be:
A(x)=x(320-2x)
A(x)=320x-2x^2
This is a quadratic with a =-2 and b=320

Maximum area will occur where x=-b/2a
=-320/(-2*2)
=80 ft
thus the width will be 80 ft and the length will be:
length=320-2*80=160 ft