
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 $\displaystyle a(x)=x^2+500$ but I really don't know if I even did that correctly.

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=5002x. The area is A=xy=x(5002x)=500x2x^2.
Differentiate that and you'll find your answer.

Thanks. Yes, its split along its height (the lines are vertical). For the perimeter I got 2y+2x=1000, though. Does it become four because of the split sections? I wasn't sure what to do with that.

1 Attachment(s)
Is it like my sketch below? If so then you have to switch x and y in my previous post. The total perimeter is 2x+4y=1000 (there's 2 horizontal lines and 4 vertical lines) and then A=500y2y^2.

Yes, it's like your sketch, thanks!