Thread: Modeling and Optimization interpretation help

I'm having a hard time what this question is asking and how it's set up:

A 216-m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. What dimensions for the outer rectangle will require the smallest total length of fence? How much fence will be needed?

I'm thinking that when it says "another fence" it means that there was already a fence there and isn't part of the total fence, but I'm having doubts. Also, a friend of mine told me theres a rectangle inscribed in a another one since the fence's are cannot be equal to the patch, but I'm guessing he interpreted wrong. If you can, may you guys give me a visual so I know what I'm dealing with? Thanks.

Originally Posted by maximade

I'm having a hard time what this question is asking and how it's set up:

A 216-m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. What dimensions for the outer rectangle will require the smallest total length of fence? How much fence will be needed?

I'm thinking that when it says "another fence" it means that there was already a fence there and isn't part of the total fence, but I'm having doubts. Also, a friend of mine told me theres a rectangle inscribed in a another one since the fence's are cannot be equal to the patch, but I'm guessing he interpreted wrong. If you can, may you guys give me a visual so I know what I'm dealing with? Thanks.

$\displaystyle A = 216 = xy$

$\displaystyle F$ is the length of fence needed ...

$\displaystyle F = 2x+3y$

get $\displaystyle F$ in terms of a single variable and minimize