A farmer has 100m of fencing to attach to a long wall, making a rectangular pen. What is the optimal width of this rectangle to give the pen the largest possible area? x 100 – 2x Area = x(100 – 2x) x y = 100x – 2x2 Sketch the graph to find max area (or complete the square for a more precise value)

Max area of 1250 when x = 25 y = -2(x2 – 50x) y = -2[(x – 25)2 – 625] A farmer has 100m of fencing to attach to a long wall, making a rectangular pen. What is the optimal width of this rectangle to give the pen the largest possible area? x y = -2(x2 – 50x) 100 – 2x y = -2[(x – 25)2 – 625] y = -2(x – 25)2 + 1250 x Max area of 1250 when x = 25