MathNet 2010 — Part 02 Question 136

There are $2n$ real numbers $a_1, a_2, \dots, a_n, r_1, r_2, \dots, r_n$ satisfying $a_1 \le a_2 \le \dots \le a_n$ and $0 \le r_1 \le r_2 \le \dots \le r_n$. Prove that $\sum_{i=1}^n \sum_{j=1}^n a_i a_j \min(r_i, r_j) \ge 0$.