What is the maximum function value? What would the dimensions be?

Question

A farmer wants to enclose 2 separate but adjacent pastures next to the river which runs along one edge of his farm: one for cows and one for sheep. He will not use fencing along the river. He has 120 m of fencing to use. What is the maximum area he can enclose?

Answer 1

Shape: Rectangle, 3 sided

Area = LW

Perimeter: P=L+2W [Doesn't matter which side is L. Do the math the other way if you doubt.]

Restrictions: P=120

Maximize area

L+2W=120, so L=120-2W

A = (120-2W)W

A = 120W-2W²

Critical point is where A' is 0

A' = 120-4W

0 = 120-4W

120=4W

30=W, L+2(30)=120, L+60=120, L=60

You have a rectangle 30x60 (1800) with one 60' riverbank.