.A rectangular lot adjacent to a highway is to be enclosed by a fence. If the fencing costs $2.50 per foot along the highway and $1.50 per foot on the other sides, find the dimensions of the largest lot that can be fenced off for $720.

Question

.A rectangular lot adjacent to a highway is to be enclosed by a fence. If the fencing costs $2.50 per foot along the highway and $1.50  per foot on the other sides, find the dimensions of the largest lot that can be fenced off for $720.

oobleck · Answer

If the highway side has length x and the other dimension is y, then we have
2.50x + 1.50(x+2y) = 720
4x + 3y = 720
so, y = (720-4x)/3
That means the area is
a = xy = x(720-4x)/3
The vertex of this parabola is at (90,10800)
So the lot is 90 by 120

As always, maximum area is achieved when the fence is divided equally among lengths and widths.