A rancher has 600 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms

Step-by-step explanation:

There's the two widths, x.

There's the four lengths, y.

4y+2x=600

Also, A=xy.

x=300-2y

A=y * (300-2y)

dA/dy=0 = y * (-2) + (300-2y)

-2y-2y+300=0

y=300/4=150/2=75

x=300-2y=300-150=150

Then the long side is 150ft, the short side is 75ft.

Check to make sure that the sum of the lengths is 600: 300+300=600

And the maximum area is 150*75 ft2