# Math Help - Mathematical Model

1. ## Mathematical Model

With 1000ft of fencing, a person wishes to fence a field into three parts as shown in the diagram. (The diagram is just a rectangle with it sectioned into three portions, y being height, x width)

How would you determine the values of x and y that give the maximum area?

** I tried to write down y in terms of x for a previous question, and I got $a(x)=-x^2+500$ but I really don't know if I even did that correctly.

2. I'm going to assume that it's split into three along its height, if it's not then just switch x and y in my explanation.

We know then that the total perimeter is 4x+2y=1000 or y=500-2x. The area is A=xy=x(500-2x)=500x-2x^2.