# A farmer has a rectangular property that needs to be fenced on three sides (a river surrounds the fourth. If he has 2400 feet of fencing material available, what maximum area will he be able to enclose?

##### 1 Answer

The dimensions that give the maximum area are

#### Explanation:

Start by tracing a diagram.

We now have:

#2x + y = 2400#

If we solve for

#y = 2400 - 2x#

Now, we know that

#A = (2400 - 2x)x#

#A = -2x^2 + 2400x#

Now differentiate with respect to

#(dA)/(dx) = -4x + 2400#

Find critical numbers.

#0 = -4x + 2400#

#x = 600#

Since

Therefore, the dimensions the give the maximum area are

We know that this is a maximum because the function

Hopefully this helps!