Question 33
Let $f(x) = (x+a)(x+b)$ where $a$, $b$ are given positive real numbers, $n \ge 2$ be a given integer. For non-negative real numbers $x_1, x_2, \dots, x_n$ that satisfy $x_1 + x_2 + \dots + x_n = 1$, find the maximum of $F = \sum_{1 \le i \lt j \le n} \min\{f(x_i), f(x_j)\}$.