A farmer wants to make a rectangular pen for his chickens. He has 1200 m of fencing. He will use one side of his barn for the pen. What dimensions will give the maximum area? What is the maximum area?

Answer 1

L + 2 W = 1200

A = L * W ... substituting ... a = (1200 - 2 W) * W = 1200 W - 2 W^2

the max area is on the axis of symmetry of the parabola
... Wmax = -b / 2 a = -1200 / (2 * -2) = 300

substitute back to find length and area