posted by Jammy .
A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and 115 feet of fencing for the remaining 3 sides. What dimensions will give her the maximum area for the pen?
if the pen has dimensions x by y, with x along the barn, then
x+2y = 115
the area a is thus
a = xy = (115-2y)y
this is a parabola, with maximum at y=115/4
so, x = 115/2
so, a pen 115/4 by 115/2 gives the maximum area