Question

A rancher with 750 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.
1] Find a function that models the total area of the four pens. (Let w be the width of the rectangular area and A(w) be the area.)

2]Find the largest possible total area of the four pens. (Round your answer to one decimal place.)

Answer 1

2 W + 5 L = 750 ft
5 L = 750 - 2 W
L = 150 - 2 W / 5
A ( W ) = W * ( 150 - 2 W / 5 )
A function that models the total area:
A ( W ) = 150 W - 2 W² / 5
A` ( W ) = 150 - 4 W / 5
150 - 4 W / 5 = 0
4 W / 5 = 150
W = 187.5 ft
The largest possible area:
A = 150 * 187.5 - (2 * 187.5² ) / 5 = 28,125 - 14,062.5 = 14,062.5 ft²