The feasible region is a triangular region, and the coordinates of the three vertices are (1, 0), (0, 1) and (3, 4) respectively.

Consider z=ax+2y, because the optimal solution must be reached at the feasible vertex, so

(1) If a=0, then z=2y, obviously there is a minimum at point (1, 0), and z=0.

(2) If a≠0, the values at (1, 0), (0, 1) and (3, 4) are respectively:

z=a

z=2

z=3a+8

Therefore, when -4

When 0

To sum up, the point at which the minimum value is reached depends on the value of a.

When restricted

-4 & lt； A<2, the minimum value exists only at point (1, 0).

So the range of a is (-4,2).