```python
def tint_mix(volume_a: int, strength_a: int, volume_b: int, strength_b: int) -> int:
    if volume_a <= 0 or volume_b <= 0 or strength_a < 0 or strength_b < 0:
        raise ValueError("Volume and strength must be non-negative integers.")
    
    total_volume = volume_a + volume_b
    total_strength = (volume_a * strength_a + volume_b * strength_b) // total_volume
    
    return total_strength
```