# Optimization Homework

I need help with this math question:

A farmer with 720 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens.

This is what I have attempted so far.

Perimeter = 2*L + 5*W = 720

Solve for W W = 144 - 2/5*L

Area of each pen = L/4*W Plug in W Area = L/4*144 - L/4*2/5*L or is it [Length/4*144 -Lenght/4*2/5lenght)

I have a feeling I am attempting this question incorrectly..

You're on the right track, but you want to maximize the total area. You've not been told that the pens are of the same size, so there's really nothing we can do with that. The total area is $$L\cdot W=144L-\frac25L^2.$$ Can you maximize that?