Question 27
(POL 2) Determine the maximum value of the sum
$$\sum_{i\lt j}x_ix_j(x_i+x_j)$$
over all $n$-tuples $(x_1,\ldots,x_n)$, satisfying $x_i\ge0$ and $\sum_{i=1}^n x_i=1$.
$$\sum_{i\lt j}x_ix_j(x_i+x_j)$$
over all $n$-tuples $(x_1,\ldots,x_n)$, satisfying $x_i\ge0$ and $\sum_{i=1}^n x_i=1$.