(4) Given that the coordinates of points $M$ and $N$ satisfy the system of inequalities $\left\{\begin{array}{l}x \geqslant 0, \\ y \geqslant 0, \\ x+2 y \leqslant 6, \\ 3 x+y \leqslant 12,\end{array} \quad \vec{a}=\right.$ $(1,-1)$, then the range of $\overrightarrow{M N} \cdot \vec{a}$ is . $\qquad$
(4) $[-7,7]$ Hint: Let $M\left(x_{1}, y_{1}\right), N\left(x_{2}, y_{2}\right)$, from the conditions we know $0 \leqslant$ $x_{1}, x_{2} \leqslant 4,0 \leqslant y_{1}, y_{2} \leqslant 3$. Therefore,
$$
\begin{aligned}
\overrightarrow{M N} \cdot \vec{a} & =(\overrightarrow{O N}-\overrightarrow{O M}) \cdot \vec{a} \\
& =\overrightarrow{O N} \cdot \vec{a}-\overrightarrow{O M} \cdot \vec{a} \\
& =x_{2}-y_{2}-\left(x_{1}-y_{1}\right) \\
& =x_{2}-x_{1}+y_{1}-y_{2} \in[-7,7],
\end{aligned}
$$

The minimum value -7 is obtained only when $M(4,0), N(0,3)$; the maximum value 7 is obtained when $M(0,3), N(4,0)$.