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Following on the example above by Markus Klein:
A gardener has 20 meters of fence-material and wants to fence a rectangle shaped garden with maximal area. Furthermore, the garden will be located next to the house such that the house will serve as one of the four walls.
The problem then reads: Maximize $f(a,b) = a*b$ subject to $2a + b = 20$.
The answer $(a ...
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