Question 154
Let $x_1, x_2, \dots, x_{22}$ be real numbers such that $2^{i-1} \le x_i \le 2^i$ holds for every $1 \le i \le 22$. Find the maximum value of
$$
(x_1 + x_2 + \dots + x_{22}) \left( \frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_{22}} \right).
$$
$$
(x_1 + x_2 + \dots + x_{22}) \left( \frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_{22}} \right).
$$