A rancher wants to make a rectangular pen to house her animals. She will divide it up with 3 fences down the middle parallel to one side. If she has 14000 ft of fencing to work with, what are the dimensions of the pen of greatest area?

Question

A rancher wants to make a rectangular pen to house her animals. She will divide it up with 3 fences down the middle parallel to one side. If she has 14000 ft of fencing to work with, what are the dimensions of the pen of greatest area? 
 Width = 
 Length =

What is the greatest area pen that the rancher can make? 
 Area =

Steve · Accepted Answer

2x+5y=14000 a = xy = x(14000-2x)/5 da/dx = 2800 - 4x/5 da/dx=0 when x = 3500 so, the pen is 3500x1400