# A farmer has 160 feet of fencing to enclose 2 adjacent rectangular pig pens. What dimensions should be used so that the enclosed area will be a maximum?

##### 1 Answer

I'm assuming that the pig pens have identical dimensions.

#### Explanation:

Let's assume that the pig pens need to be fenced in the way shown in the diagram above.

Then, the perimeter is given by

The area of a rectangle is given by

Now, let's differentiate this function, with respect to y, to find any critical points on the graph.

Setting to 0:

Hence, the dimensions that will give the maximum area are

A graphical check of the initial function shows that the vertex is at

Hopefully this helps!