Question 99
Let $n \ge 3$ be integer. Suppose that $\alpha, \beta, \gamma \in (0, 1)$ and $a_k, b_k, c_k \ge 0$ $(k = 1, 2, \dots, n)$ satisfy $\sum_{k=1}^n (k+\alpha)a_k \le \alpha$, $\sum_{k=1}^n (k+\beta)b_k \le \beta$ and $\sum_{k=1}^n (k+\gamma)c_k \le \gamma$. Find the minimum of $\lambda$ such that $\sum_{k=1}^n (k+\lambda)a_k b_k c_k \le \lambda$.