Question

Matlab a farmer wishes to build a rectangular pen for his animals out of 40 feet of fencing what should be the length and width of pen so that its area is as great as possible

Answer 1

width=w
length=(40-2w)/2=20-w
A=w(40-w)
A=40w-w²
A'=40-2w=0
2w=40
w=20

20x20 is the size of the pen having the greatest area. this tells us the largest rectangle for a given perimeter is a square