A fence is to be built to enclose a rectangular area of 220 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 13 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

Answer 1

a and b are lengths

A = 220 = a * b so a = 220/b

cost = 2(6a) + 1 (6b) + 1(13b)
cost = c = 12 a + 19 b
c = 12(220/b)+19 b
dc/db = 0 at max or min = 12(-220/b^2) + 19

220(12) = 19 b^2
solve for b and a