Question

A rancher wants to make an animal pen by fencing in an area of 2500000 square feet in a rectangular field and then divide it up with 5 fences down the middle parallel to one side. The rancher wants to use the shortest total length of fencing possible. If she accomplishes that, what will be the dimensions of the pen? What is the width, length, and total fencing used

Answer 1

if width=x and length=y, the perimeter
p = 7x+2y
The area a is
xy = 2500000
x(p-7x)/2 - 2500000 = 0

7x + 2(2500000/x) = p
take derivative:
7 - 5000000/x^2 = 0
x^2 = 5000000/7

x = 845.15
y = 2958.0
p = 7x+2y = 8874 ft