If you have 100 feet of fencing and want to enclose a rectan

Solution

We have a rectangle of sides x and y. Since it\'s against a wall, we only consider three walls, two walls of length x and one of length y.

Thus, the length of fencing equation is:

100=2x+y

And the volume equation to maximize is:

V=x*y

Solve the first equation for y to get:

y=100-2x

Plug this in to the volume equation to get:

V=x*(100-2x)=100x-2x^2

Find the maximum of this function by taking the derivative:

V\'=100-4x = 0

This is zero when x=25. Therefore, y must be 50.

Thus, the area is 25*50 = 1250 ft^2