Question

A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 1600 yards of fencing, what dimensions will give the maximum rectangular area? yd(smaller value)? yd (larger value)?

Answer 1

If the field has dimensions x and y, and two extra length of y are used inside the field,

2x+4y = 1600
so, x = 800-2y

the field's area is

a = xy = (800-2y)(y)
= 2y(400-y)

This is a parabola with vertex at y=200, so the maximum area is achieved when the field is 400x200