Lines, Parabola, and Systems

Question

A building contractor wants to fence in a rectangular plot adjacent to a straight highway using the highway for one side, which will be left unfenced. If the contractor has 500 feet of fence, find the dimensions of the maximum enclosed area.

Answer 1

Area = A= LW

Perimeter = L+2W = 500

L= 500-2W

A =(500-2W)W = 500W-2W^2

take the derivative and set = 0

A' = 500-4W = 0

4W = 500

W = 500/4 = 125 feet wide

L= 500-2W = 250 feet long

max A = 125(250) = 31,250 ft^2