How would I answer this question?

Question

If you have 3000 feet of fencing and you want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? You do not have to fence the part of the area facing the wall.

Answer 1

Let x = length of fence parallel to the wall and let y = length of each side of fence that is perpendicular to the wall.

Then, x + 2y = 3000, so y = 1500 - 0.5x

Area = A = xy = x(1500 - 0.5x)

The graph of the area function is parabolic with x-intercepts at 0 and 3000. The maximum occurs halfway between the x-intercepts.

So, maximum area when x = 1500 ft and y = 750 ft

Maximum area = xy = 1,125,000 square feet