Final answer:
A company moving towards a line-and-staff structure would categorize its production department as a line function. This is because it's directly involved in creating the company's products, which is typical of a line function in this organizational structure.
Step-by-step explanation:
A company evolving from a line to a line-and-staff structure would classify its production department as a line function. In a line-and-staff organization, line functions are those that are directly involved in the primary revenue-generating activities of the company, such as production and sales, and are distinct from staff functions that provide support and advice. As companies grow, they tend to develop more complex organizational structures to cope with increased operational demands, which often involves the creation of specialized roles and departments that contribute to efficiency and productivity gains.
For example, workers on an assembly line exemplify a division of labor, which is a hallmark of the line function. These workers are trained to complete specific tasks, contributing directly to the creation of the company's products. The efficiency brought by such divisions of labor allows for more finished goods to be manufactured with greater speed. However, as a company progresses from Stage 1 to Stage 2 in its growth, production output continues to rise but at diminishing returns, signaling the need for additional roles that may not be directly involved in production but are crucial for supporting the increasing complexity of operations.