Let $(x_1^* = 1, \ x_2^* = 0, \ x_3^* = 2)$ be an optimal solution of the linear programming problem
\[
\text{Minimize } \quad x_1 + 5x_2 + 2x_3
\]
subject to
\[
\begin{cases}
x_1 - x_2 \le 1, \\
x_1 + x_2 + x_3 \ge 3, \\
x_1, x_2, x_3 \ge 0.
\end{cases}
\]
If $(\lambda_1^*, \lambda_2^*)$ is an optimal solution of its dual, then
