You have 800 ft of fencing to make a pen for hogs. If you have a river on one side of your property, what is the dimension of the rectangular pen that maximizes the area?
lenpol7
For any given dimensions a square has the largest area. This can be proved by calculus.
So if we divide 800 ft by 3 , then 266.66...ft is the length of on side. So three sides each of 266.666...ft plus the river bank of 266.666....ft will give a square.
266.666 .ft x 266.666 .ft = 71,111.111.... sq.ft. is the area.
jacob s
let the length =x
breadth=y
x + 2y=800
x=800-2y
Area=xy
=(800-2y)y
=800y-2y2
For maximum area dA/dy=0
dA/dy=800-4y
800-4y=0
y=200
x=800-2(200)
=400
Dimensions are length=400 ft and breadth=200 ft
zipper
Being pigs can swim you ned the fence all the way around, and the over all size is based on the wire you have and space you have. You could make a square which would be 200 by 200, or rectangle were it is 300 by 100 feet: that is up to the space you have to put the fence!
Gypsyfish
Do you know that hogs won't go into the water and drown? This a variation on the classic "puppies in a pen problem". With fencing- or any area- the closer you get to a square, with all sides even, the more area you will have in the enclosure.
Krishnamurthy
You have 800 feet of fencing to make a pen for hogs.
If you have a river on one side of your property,
what is the dimension of the rectangular pen
that maximizes the area?
L + 2W = 800 feet