A fence is to be built to enclose a rectangular area of 320 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

Answer 1

If the cheap sides are x, and the expensive side is y, then
xy = 320
c(x) = 6*2x + 6y + 14y = 12x+20y
= 12x + 20(320/x)

c'(x) = 12 - 6400/x^2
minimum cost is at x = 80/√12 ≈ 23

So, the area is roughly 23 by 14
(That's 322 ft^2)