```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")
    
    # Check if the run would pass the last column
    if col + length > len(floor[row]):
        raise ValueError("the run would leave the plan")
    
    # Check if any cell in the run is not open
    for i in range(length):
        if floor[row][col + i] != '.':
            raise ValueError("a cell in the run is not open")
    
    # Write the conveyor run cells
    cells = list(floor[row])
    for i in range(length):
        cells[col + i] = '='
    
    # Return the plan with only that row changed
    return [cells] + floor[1:]
```