A fence is to be built to enclose a rectangular area of 310 square feet. The fence along three sides is to be made of material that costs 3 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

Let two of the sides be x ft each
let the other two sides by y ft each

xy = 310
y = 310/x

cost = 3(2x) + 3y + 14y
= 6x + 17y
= 6x + 17(310/x)
= 6x + 5270/x
d(cost)/dx = 6 - 5270/x^2
=0 for a min of cost
6 = 5270/x^2
6x^2 = 5270
x^2 = 878.333..
x = √878.333
= appr 29.64 ft
y = 310/29.64 = 10.46