A rancher wants to fence in an area of 2000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

Answer 1

fence length = z = 3 x + 2 y
x y =2*10^6 ft^2
so
z = 3(2*10^6/y) + 2 y
z = 6*10^6/y + 2y
dz/dy = -6*10^6/y^2 + 2 y
= 0 for max or min
y^3 = 3*10^6
y = 3^(1/3) *100
y = 144 ft
x = 13889 ft
need length = 3x+2y