Optimization at a fixed cost.

[Ian McPherson]

I have never seen a problem like this before.

A rectangular area is to be enclosed and divided into thirds. The family has $800 to spend for the fencing material. The outside fence costs $10 per running foot installed, and the dividers cost $20 per running foot installed. What are the dimensions that will maximize the area enclosed?


So this is the picture i think it should look like

I know that i will need an equation for area and an equation for perimeter. However, I'm not sure where to assign the variables to. Would I assign all the lines running left to right an x value and the up and downs a y? such as P = 20x + 60y? or would all the lines on the outside be 10x and on the inside 20y?

 

[pka]

You want to maximize \(\displaystyle A=xy\)
Where \(\displaystyle 20x+60y=800\) or \(\displaystyle x=40-3y\).