# Mathematical Model

• Feb 17th 2009, 10:38 AM
rebak
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.
• Feb 17th 2009, 10:48 AM
JD-Styles
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.

Differentiate that and you'll find your answer.
• Feb 17th 2009, 10:51 AM
rebak
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.
• Feb 17th 2009, 11:13 AM
JD-Styles
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=500y-2y^2.
• Feb 17th 2009, 11:25 AM
rebak
Yes, it's like your sketch, thanks!