Question

You have been hired by the Humane Society to construct six animal cages using 1400 feet of chain fence. Express the length and width using function notation. Include a graph with the area function with explanation of significance. Find the dimensions that maximize the total enclosed area and the relevant domain and range.

Answer 1

You need to specify more about the layout of the cages. Are they all stand-alone? Do they share sides in some way?

Answer 2

It's a 2x3 cage making the 6 cages

Answer 3

In that case, if each cage has width x and length y, the total fencing used is

9x+8y = 1400

and the area is

a = 6xy

But we know that y = (1400-9x)/8, so

a = 6x(1400-9x)/8 = 1050x - 27/4 x^2

That is just a parabola, with its vertex at x = 700/9

So, y = 700/8

You can finish up the other details.

Note that as usual in such problems, the fencing is divided equally among the lengths and the widths.