# Optimization: Fence Problem 1

- Author:
- hpp3

A farmer needs to enclose a field with a fence. She has 10 meters of fencing material. Determine the dimensions of the field that will enclose the largest and smallest areas.

Instructions:

- Drag the purple 'X' or use the 'Show Animation' and 'Stop Animation' Buttons to change the dimensions of the field.
- Click the check box 'Show Area' to show or hide the calculated area.

*Make a Prediction*: Determine the dimensions of the field that will enclose the largest area. What shape is this field?- Check your predictions by changing the dimensions of the field until the calculated area is the greatest.

*Make a Prediction*: Determine the dimensions of the field that will enclose the smallest area. What shape is this field?- Check your predictions by changing the dimensions of the field until the calculated area is the smallest.

- What is the domain for this problem? That is, what are the possible values for the
*width*of the field? - What is the range for this problem? That is, what are the possible values for the
*height*of the field? - Write an equation for the amount of fence the farmer has (this is your
*constraint*). - Write an equation for the area of the field (this is what your are
*maximizing*or*minimizing*).