I have a task to write a dual program for the following primal:
maximize $x_1 + 2x_2 + 3x_4$
subject to
$x_2 - 6x_3 + x_4 \leq 4 $
$x_1 + 3x_2 - 3x_3 = 0$
$6x_1 - 2x_2 + 2x_3 - 4x_4 \geq 5$
$x_2 \leq 0$, $x_4 \geq 0$
However, $x_1$ and $x_3$ variables are not under a constraint (there is no limiting constraint $x_i \geq 0$ or $x_i \leq 0$ or $x_i \in \mathbb{R}$).
How should I proceed? Should I assume that $x_1, x_3 \in \mathbb{R}$ and put "=" signs to first and third constraints?