A rancher has 640 feet of fencing with which to enclose two adjacent rectangular corrals . What dimensions should be used so that the enclosed area will be a maximum?

Answer 1

I make the assumption that the rectangles are side-by-side and have lengths l1 and l2 with the same w.

A =( l1 + l2)w and P = 3w + 2(l1 + l2) but l1 and l2 can be combined to L = l1+ l2 (where the fence is between the rectangular regions does not affect the area.

A = LW P = 3w + 2L = 640 (ft of fence)

Solve perimeter equation for L in terms of w and sub into area equation

Find w so that dA/dw = 0.

Plug into either equation to solve for L

I apologize if that wasn't the setup.