A rancher has 900 meters of fence to enclose a rectangular corral. The corral is to be divided into four subcorrals. What are the overall dimensions of the large enclosure that yield the maximum area?

Answer 1

let the width of each smaller enclosure be x
let the length of each smaller enclosure be y

So 8x + 2y = 900
y = 450 - 4x

Large area = A = 4xy
= 4x(450-4x)
= 1800x - 16x^2
dA/dx = 1800 - 32x
= 0 for a max of A

32x = 1800
x = 56.25 and y = 450 - 4(56.25) = 225

So the large enclosure is 4x by y
or 225 by 225

(no surprise that the large field would be a square, usually this type of question has one side against a barn or a river)