A farmer wants to fence an area of 16000 square feet and the

A farmer wants to fence an area of 16000 square feet and then divide it into four parts by placing three parallel fences to one of the sides of the rectangle. What is the dimensions of the rectangle that minimize the cost of the fence?

Solution

we have, Area = xy = 16000 now, Length of fence = 2(x+y) + 3y L = 2x + 5y L = 2x + 5 ( 16000/x) L = 2x + 80000/x dL/dx = 0 2 - 80000/x^2 = 0 x^2 = 40000 x = 200 hence Length = x = 200 feet Breadth = y = 80 feet