a farmer wants 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 only afford 1000 yards of fencing, what dimensions will give the maximum rectangular area?

Answer 1

Make a sketch
let the length of the whole field be y yds
let each divider line be x yds

so 2y + 4x = 1000
y = 500 - 2x

area = xy
= x(500-2x)
= 500x - 2x^2

I will assume you are taking Calculus, if not you will have to complete the square on the above

d(area)/dx = 500 - 4x = 0 for a max area
4x=500
x = 125
then y = 250

The whole length should be 250 yrd , and each smaller pen should be 125 yrds wide.
max area = 125(250) = 31250 yds^2