1. 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)

2. 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) x
Max area of 1250 when x = 25