A buggalo farmer wants to pen in as large an area as possible, he has 560 feet of fencing. He will be constructing the pen against his barn, so he only needs to use fencing on 3 sides of the pen. Find the dimensions that maximize the area of the pen.
A = L * W
L + 2 W = 560 ... L = 560 - 2 W
substituting ... A = (560 - 2 W) * W = -2 W^2 + 560 W
the max area is on the axis of symmetry ... -b / 2a
Wmax = -560 / (2 * -2) = 140
substitute back to find L ... one L is the side along the barn