Find the dimensions of the rectangular corral producing the greatest enclosed area split into 3 pens of the same size given 500 feet of fencing.

Total fencing = 500 feet

x + x + x + x + y + y = 500

2y + 4x = 500

Y + 2x = 250

Y = 250 – 2x

Now, area,

A = (x) (y)

A = (x) (250 – 2x)

A = 250x – 2x^2

dA/dx = 0 for maximum area

d/dx (250x – 2x^2) = 0

250 – 4x = 0

4x = 250

X = 62.5

Y = 250 – 2 (62.5) = 12.5

Hence, the dimension of the rectangular area are :

Length y = 125 feet

Width w = 62.5 feet

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