Math Word Problem

Question

A Farmer has 480 ft of fencing and wants to enclose two adjacent rectangular corrals for the pigs and goats. What size corrals will yield the maximum area.

Answer 1

Create a diagram of the adjacent rectangular pens with width, W, and length, L.

The perimeter of these enclosures requires 2 sections of width and 3 sections of length.

Thus p = 2W + 3L = 480 and isolating w gives W = (- 3/2L + 240)

A = LW = -3/2L² +240L

A^' = -3L + 240 = 0 ; L = 80 , W = 120 and the maximum area enclosed = 9,600 ft². Each adjacent corral is 60' x 80'.