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.
3 answers
You need to specify more about the layout of the cages. Are they all stand-alone? Do they share sides in some way?
It's a 2x3 cage making the 6 cages
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.
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.
1 answer