A farmer wants to build a barn with one internal wall. One meter of external wall costs $200 and one meter of internal wall costs $80. The farmer wants to construct the barn with the largest possible area and only has $7200 to spend on walls. What dimensions should the farmer choose?

Answer 1

If there are 3 walls of length x and 2 of length y
that is, the internal wall is of length x, then
200(2x+2y) + 80x = 7200
480x + 400y = 7200
6x+5y=90
The area is
a = xy = x(90-6x)/5 = 6/5 x(15-x)
Since the vertex of the parabola is midway between the roots, maximum area is at x=15/2, y=9