calculus, area, derivatives

Question

 A fence is to be built to enclose a rectangular area of 280 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 16 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

Dimensions?

Answer 1

Let x = the length of the fence made from cheaper material,

then 280-x is the length at the higher price.

The cost will be 3x + 16(280-x).

The value of x which will yield the lowest cost will be obtained by setting the derivative of the cost function = to zero and solving that equation for x.

Good luck!