Optimization problem...?

Question

A rancher wants to fence in an area of 500000 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

x*y=500,000
3x+2y=z ( minimum)
y=500,000/x
so z= 3x+10^6/x
z´= 3-10^6/x^2=0 so x^2= 10^6/3 and x = 1000* 1/3 *sqrt(3) feet
length = 1000*sqrt3+1000*sqrt(3) = 2000*sqrt(3)feet