Determine maximum value

Algebra Level 3

For some positive reals satisfying i=124xi=1\displaystyle{ \sum_{i=1}^{24} x_i=1}, determine the maximum possible value of (i=124xi)(i=12411+xi).\displaystyle{ \left (\sum_{i=1}^{24}\sqrt{x_i} \right ) \left (\sum_{i=1}^{24} \frac{1}{\sqrt{1+x_i}} \right )}.

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