Evaluate: $x_i\ge0; \max_{1\le i \le n , \sum_{i=1}^{n}{x_i=a}}x_1x_2...x_n$

Question

Let a be a fixed positive real number.Evaluate: $$x_i\ge0; \max_{1\le i \le n , \sum_{i=1}^{n}{x_i=a}}x_1x_2...x_n$$

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I guess it should be $x^n$ where $x=\frac{a}{n}$since this is true for $n=2$, I have generalise the case only. Am I right?

Answer 1

Use A.M.$\geq$ G.M. for the n numbers...............