If there is 800 800 feet of fencing available, what is the maximum possible area of the pasture?

Question

The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is feet of fencing available, what is the maximum possible area of the pasture?

answer in square feet

Answer 1

Let x = length of the side parallel to the creek and let y = length of each of the other two sides.

Then, x +2y = 800. So, x = 800 - 2y

Area = xy = (800 - 2y)(y) = -2y² + 800y

The graph of A is a parabola opening downward with maximum when y = -800 / (2(-2)) = 200

Maximum area when y = 200 and x = 800 - 2y = 400

Maximum area = xy = (400)(200) = 80000 sq ft