The back of George’s property is a creek. George 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 140 feet of fencing available, what is the maximum possible area of the pasture?
Let the one side parallel to the creek be x ft
let each of the other two sides by y ft
restraint: 2x + y = 140 or y = 140-2x
area = xy = x(140-2x) = -2x^2 + 140x
all we need is the vertex of this downwards opening parabola
the x of the vertex is -b/(2a) = -140/-4 = 35
then max area = -2x^2 + 140x = -2(1225) + 140(35) = 2450 ft^2