Question

A contractor is to build a warehouse whose rectangular floor will have an area of

20002000

square feet. The warehouse will be separated into two rectangular rooms by an interior wall. The cost of the exterior walls is

​$200200

per linear foot and the cost of the interior wall is

​$175175

per linear foot. Express the​ contractor's cost for building the​ walls, C, as a function of one of the dimensions of the​ warehouse's rectangular​ floor, x.

c(x)=

Answer 1

Let length of the floor is x feet and width of the floor is y feet.

Then as area is 2000 square feet so width of the floor(y) will be (2000/x) feet which implies,

Now for interior wall, length = x
So, total cost(C₁​​​​​) = 175x

And for exterior wall, length = perimeter of rectangular floor = 2(x + y)
So, total cost(C₂​​​​​) = 200*2(x + y) = 400(x + y)

So, contractor's cost for building walls, C(x) = C₁​​​​​​ + C₂
i.e. C = 175x + 400(x + y)
i.e. C = 175x + 400x + 400y
C = 575x + 400y
C = 575x + 400(2000/x)
C = 575x + (800000/x)