1) When cutting by the second cutting method, the length of two A-type plates is 120cm, 150- 120 < 30, so the B-type plate cannot be cut.

When cutting by the third cutting method, the lengths of the three B-shaped plates are 120cm and 120 < 150, respectively.

But the length of four B-shaped plates is 160 cm > 150, so it is impossible to cut four B-shaped plates.

∴m=0,n=3；

2) Type A plate: 240=X+2Y B plate: 180=2X+3Z.

3) Q=X+Y+Z is obtained from 2) y =120-1/2xz = 60-2/3x.

∴Q=- 1/6X+ 180. Like the first method, X=90 can satisfy the number of B-type plates, so X≤90.

Because q is a linear function that decreases with the increase of x, when x takes the maximum value, q is the minimum, that is, X=90 Q= 165.