Question 14
Determine the largest value the expression $\sum_{1 \le i \lt j \le 4} (x_i + x_j) \sqrt{x_i x_j}$ may achieve, as $x_1, x_2, x_3, x_4$ run through the non-negative real numbers that add up to $1$. Determine also the $x_i$ at which the maximum is achieved.