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?
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 ftÂ
