Question

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?

Answer 1

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