SMO 2002 Problem 2

Let $a_1,a_2,...,a_n$ and $b_1,b_2,...,b_n$ be real numbers between $1001$ and $2002$ inclusive. Suppose $\sum_{i=1}^n a_i^2= \sum_{i=1}^n b_i^2$ . Prove that $$\sum_{i=1}^n\frac{a_i^3}{b_i} \le \frac{17}{10} \sum_{i=1}^n a_i^2$$ Determine when equality holds.