```python
"""Lay a straight eastward conveyor run across a factory floor plan."""

def lay_conveyor(floor: list, row: int, col: int, length: int) -> list:
    if row < 0 or row >= len(floor):
        raise ValueError("the run starts off the plan")
    
    if col + length > len(floor[0]):
        raise ValueError("the run would pass the last column")
    
    if any(cell != '.' for cell in floor[row][col:col + length]):
        raise ValueError("some cells the run covers are not open")
    
    cells = list(floor[row])
    cells[col:col + length] = ['='] * length
    return [cells] + floor[row+1:]
```