[michaela_mooney17]

A farmer uses 400m of fencing to create a rectangular pig pen and to divide it into four equal regions. Algebraically determine the function which gives the area of the pig pen as a function of its width, and state the dimensions that produce maximum area.

How do I start this off.. can anyone help me ?

[asterisk_man]

Start by drawing a picture:

  <----w---->
/\+----+----+
| |    |    |
| |    |    |
h +----+----+
| |    |    |
| |    |    |
\/+----+----+

Now write an equation for the length of fence used:
3*w+3*h=400

Now write an equation for the area of the pen:
A=w*h

Solve the first equation for h so we can substitute it into the second (since the problem wants the equation in terms of w only).

3w+3h=400
3h=400-3w
h=400/3 - w

Substitute this into the second equation:

A=w*h
A=w*(400/3 - w)
A=(400w/3)-w^2

From here you should be able to solve for the width that gives the max area.