The feasible region determined by the system of constraints, 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, and y ≥ 0, are as follows.

The corner points of the feasible region are O (0, 0), A (2, 0), B (0, 3), and C(20/19,45/19)
The values of Z at these corner points are as follows.

Therefore, the maximum value of Z is 235/19 at the point (20/19,45/19)