Question

A farmer has 2,400 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Write the function that will produce the largest area if x is the short side of the rectangle.

Answer 1

2x+y = 2400
so, y = 2400-2x

a = xy = x(2400-2x) = 2400x-2x^2
That is just a parabola, with vertex at x=600

So, the field is 600 x 1200

As usual, these problems achieve maximum area when the perimeter is divided equally among lengths and widths.