Question

A construction company has adjoined a 3600 ft^2 rectangular enclosure to its office building. Three sides of the enclosure are fenced in. The side of the building adjacent to the enclosure is 360 ft long and a portion of this side is used as the fourth side of the enclosure. Let x and y be the dimensions of the enclosure, where x is measured parallel to the building, and let L

be the length of fencing required for those dimensions.

(a) Find a formula for L
in terms of x and y

.

L(x,y)=

(b) Find a formula that expresses L
as a function of x

alone.

L(x)=

(c) What is the domain of the function in part (b)? Express as an interval.

Answer 1

I will set it up for you, then you can dig out the parts that fit into
each question

As you suggest, let the length of the enclosure by x
and its width be y
So we need (x + 2y) ft of fencing, since we only need 1 length.

We are told that xy = 3600 , or y = 3600/x

So L = x + 2y
= x + 2(3600/x) = x + 7200/x

Since this is Calculus, I will assume that there is more to this question
such as we are given the cost of the fencing.
A typical follow-up would be to find the dimensions of the enclosure
for a minimum cost of the fencing.