Calculus Problem

Question

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 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that result in the enclosure having the minimum cost to construct.

Answer 1

Let l be the length of the enclosure and w be the width, both in feet. (l and w are interchangeable)

Then we know that

lw = 320.

We're trying to minimize the cost. The two widths we'll say, cost $3 per foot so the cost of both is 3w

The cost of the lengths is $3 per foot for one of them and $14 per foot for the other. So one costs 3l and the other costs 14l

So the cost of the entire enclosure is 3w + 3w + 3l + 14l = 6w + 17l.

Do you think that you can solve the rest?