```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[row]):
        raise ValueError("the run would pass the last column")
    cells = list(floor[row])
    for i in range(length):
        if cells[col + i] != ".":
            raise ValueError("the run covers a cell that is not open")
    floor[row] = floor[row][:col] + "=" * length + floor[row][col + length:]
    return floor
```