I am still learning, but still I wanted to try it, so..
Let x and y be length and breadth of the barn.
Given in figure and your description, x + 3y = 3600 => y = (3600 - x)/3,
Therefore, Area occupied by the fence, A = x * y = x * (3600 - x)/3= (3600x - x²)/3
So the max area is when dA/dx = d/dx {(3600x - x²)/3} =0 => x = 1800
so, x =1800 and y = (3600 -1800)/3 = 600
So, Max area A = x* y = 1800 * 600 = 1080000
Since two equal pens must be created, Therefore the area of a single pen = 1080000/2 = 540000 sq. unit