as always, maximum area is when the fence is divided equally among lengths and widths. So, since I cannot see the diagram, but it implies the pens are in a row, we have six pens of length x and width y.
2x+7y = 540
area = 6xy = 6(540-7y)/2 * y
= 1620y - 21y^2
This is a parabola with vertex (maximum area) at y=270/7
So, each pen is 135 by 270/7
Note how the fence is equally divided among lengths and widths.
A cattle rancher wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). There are 540 feet of fencing available to complete the job. What is the largest possible total area of the six pens?
1 answer
1 answer