Calculus Problem Help

Question

A cattle rancher wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the rectangle (see the figure below). There are 670 feet of fencing available to complete the job. What is the largest possible total area of the three pens? 

Answer 1

4w + 2L = 670

2w + L = 335

L = 335 - 2w

Area A(w) = w(335 - 2w)

max occurs at the average of the solutions.

solutions are w=0 and w = 167.5

the average is 83.75

83.75 * (335 - 2 * 83.75) = 14028.125