Question 161660
a farmer has $3000 to spend on fencing material to enclose a pasture.if the fencing material costs $15 per yard, what is the maximum area he can enclose in square feet?
-----------------
He can buy 200 yards of fence (3000/15), which is 600 feet.
-----------
The maximum area for a given perimeter is enclosed by a circle.  In this case, the circle will have a circumference of 600 feet.
The radius is 600/2PI = 300/PI
The area = PI*r^2
Area = PI*(300/PI)^2
Area = 90000/PI = 28,648 sq feet.
-------------
If it's a rectangular pasture, a square has the max area for 4-sided figures.
The square would be 150 by 150,
Area = 22,500 sq feet (less than the circle)