A farmer has 1600 feet of fence

Question

A farmer has 1600 feet of fence and wants to enclose a rectangular field with two internal fences parallel to one side, as shown below. What are the dimensions that would maximize the area? Make sure you check that the total amount of fencing is 1600 and that the area is maximized.

Answer 1

2x +y = 1600

y = 1600 -2x

Area = XY = x(1600-2x) = 1600x -2x^2

take derivative, set = 0

A' = 0 = 1600-4x, x = 400 feet

y =800 feet

max A = XY = 400(800) = 320000 square feet