A rancher with 550 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure)

Question

(a) Find a function A that models the total area of the four pens. (Use w to represent the width of the field.)

(b) Find the largest possible total area of the four pens.

Thanks!

Answer 1

2 lengths = 550 - 5 widths

1 length = 275 - 2.5 width

Area = w(275 - 2.5w)

Area = -2.5w² + 275w

Maximum at w = 55 (Max, occurs at -b / 2a)