a farmer wants to make a rectangular pen from 200 feet of fencing. he plans to use a 100 foot wall along with some of the fencing to make one side of the pen. find the dimensions of the pen that will make the enclosed area as large as possible.

Answer 1

presumably, he wants to use all of the fencing, if he wants as large a pen as possible...

2x+y=200
a = xy = x(200-2x) = 200x-2x^2
da/dx = 200-4x
da/dx=0 when x=50

the pen is 50x100

In this kind of problem, the fencing is always divded equally among the lengths and widths.