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!