Question

Matt wants to build a rectangular enclosure for this animal. One wide of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Matt has 1000 feet of fencing. You can find the dimensions that maximize the area of the enclosed.

Answer 1

500 feet by 250 feet.

Explanation:

Let the length be x and the width y feet.

As we have 1000 feet of wire:

x + 2y = 1000

2y = 1000 - x

y = 500 - 0.5x

So the area = x(500 - 0.5x)

A = 500x - 0.5x^2

For a maximum area the derivative

A' = 500 -x = 0

x = 500 feet.

2y = 1000 - 500

y = 250 feet.