A simple use of Calculus
You're fencing in a rectangular garden against a wall. So no fence is needed along the wall.
You have 100 feet of fencing. What size do you make the garden to maximize its area?
Let the garden be y deep and x wide.
So its area is a=xy
The length of fencing is l=2y+x=100
So x=100-2y
Substitute this into the area, so a=y(100-2y)=100y-2y^2
Differentiate and set to zero to find the max..
da/dy=100-4y=0
So y=25
Which means the garden is 25 deep and 50 wide.
Content written and posted by Ken Abbott abbottsystems@gmail.com
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