You have 800 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river,find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

Answer 1

I know how to do this with calculus, but algebraically it starts the same way.

L + 2W = 800 L = 800 - 2w
A = LW

A= (800-2w)w

A = 800w - 2w^2

Take the derivative: 800 -4w
800 -4w = 0 to find max.
800 = 4w
200 =w
l = 400

Answer 2

Thank you!

Answer 3

How did it become 800-4w from 2400-2w^2?