Farmer Jones wants to build a recangular pen with three equalparts. He has 200 feet of fencing. What dimensions willproduce the largest pen?

Answer 1

Length = 3 x, width = y
4 y + 6 x = 200 so y = (200-6x)/4
or y = (100 - 3x)/2
A = area of one of the three sections = x y

A = x (100-3x)/2 = 100 x/2 - 3 x^2/2

-2 A = 3 x^2 - 100 x

-(2/3)A = x^2 - (100/3)x

x^2 - (100/3)x + 2500/9 = -(2/3)A + 2500/9

(x - 50/3)^2 = -(2/3)A + 2500/9

(x - 50/3)^2 = -(2/3)[A - 416 2/3 ]

x = 50/3
3 x = length = 50
y = (100-3x)/2 = 25
total area = 50*25 = 1250
area of each pen = 1250/3 = xy = 416 2/3