You have 276 feet of fencing to enclose a rectangular region. What is the maximum area?

The perimeter is

P = 2L + 2W or

80 = 2L + 2W

dividing by 2 we get

40 = L + W

THe area is

A = LW

solving for L, we get

L = 40-W

substituting that in, we get

A = (40-W) (W)

using completing the square, we get

A = - (W-20) ^2 + 400

So, when W = 20, the max area is 400.