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Maximum Product of Positive Numbers with Fixed Sum
If:
$$x_1+x_2+\cdots+x_n=S$$
then:
$$x_1x_2\cdots x_n\leq\left(\frac{S}{n}\right)^n$$
Equality occurs when:
$$x_1=x_2=\cdots=x_n=\frac{S}{n}$$
Usage
- Used for direct optimization of products under a fixed-sum condition.
