2. Given $a>0, x, y$ satisfy the constraint conditions $\left\{\begin{array}{l}x \geqslant 1, \\ x+y \leqslant 3, \\ y \geqslant a(x-3) .\end{array}\right.$ If the minimum value of $z=2 x+y$ is 1, then $a=$
Given that $a>0$, the target line slope $k=-2$, combining with the graph, when $z=2 x+y$ passes through the point $(1,-2 a)$, it achieves the minimum value, i.e., $2-2 a=1 \Rightarrow a=\frac{1}{2}$.