Maximize Area using quadratic functions

Question

A rectangular field is to be enclosed with a fence. One side of the field borders a road, and the fencing material to be used for that side costs $8 per foot. The fencing material for the remaining sides cost $6 per foot. Find the maximum area that can be enclosed for $1600.

Answer 1

Let R=the length of the fence by the road and F the length of the other side (the field)

8R + 6(R+2F) = 1600

14R + 12F = 1600

7R + 6F = 800

F = (800-7R)/6

Area = RF = (800R-7R²)/6

At maximum 14R = 800 and 12F=800.

I am always uneasy when these problems don't work out with nice answers, but I think this is correct.