Minimization of product function subject to constraints

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I want to minimize the following function:

$\prod_{i=1}^{n}{x_i}$

Subject to the following constraints:

$\sum_{i=1}^{n}{x_i}=1.1+(n-1)(0.1)$ and $0.1 \leq x_i \leq 1.1$

How should I go about it? I am trying to check if the minimum value is achieved when one of the $x_i$'s is 1.1 and everyone else is 0.1.