Determine maximum value

Algebra Level 4

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

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