A farmer has decided to build a pen for his horse alongside a drainage canal.

Question

A farmer has decided to build a pen for his horse alongside a drainage canal. If the pen is to be

rectangular in shape and he has 400 feet of fencing available, what is the area of the largest possible pen he

can create? He doesn’t need to have fencing on the canal side of the pen.

Answer 1

400 = 2W + L

L= 400-2W

Area = A = LW = (400-2W)W = 400W -2W^2

take the derivative, set it = 0 and solve for W to get max area

A' = 400- 4W = 0

4W = 400

W = 400/4 = 100 feet

L = 400-2W = 400-200 = 200 feet

dimensions are 100 x 200 feet

Max Area is 100x200 = 20,000 square feet

(Had you need fences on all 4 sides, the maximum area would have been from a square with dimensions 100 by 100 feet, and max area = 10,000. Eliminating one side doubled the max area)