120 feet of fencing to enclose 3 adjacent corrals

Question

We have 120 feet of fencing to enclose three adjacent rectangular corrals with one side against a wall. Find the dimensions of the rectangles whose area is as large as possible.

Answer 1

We are forced to assume the rectangular corrals have the same dimensions...

So for width w and length L

2w + 3L = 120 ---> 3L = 120 - 2w ----> L = (120 - 2w)/3 = 40 - (2/3)w

Area = length * width

= (40 - (2/3)w) * w

The max occurs at the AVERAGE of the solutions of this quadratic function.

The solutions are w=0 and 40 - (2/3)w = 0

-(2/3)w = -40

w = 40*3/2 = 60

Their average is 30.

The dimensions are w=30 and length = 20

Max area is 600