It is known that variables X and Y satisfy the constraints of 1≤x+y≤4, -2 ≤ x-y ≤ 2.

Draw the feasible region in the coordinate system,

The figure shows a quadrilateral ABCD, where a (3, 1),

kAD= 1，kAB=- 1，

Z in the objective function z=ax+y (where a > 0) represents the intercept in a linear system with a slope of -a,

If the maximum value is obtained only at point (3, 1),

Slope should be less than kAB=- 1,

exactly

So the range of a is (1, +∞).