The correct answer is: C. staff function.

Personnel management is essentially a staff function because it provides support and advice to line managers, who are responsible for the day-to-day operations of the organization. Personnel managers typically work in human resources departments and are responsible for tasks such as recruiting, hiring, training, and developing employees. They also play a role in employee relations, compensation, and benefits.

A line function is a primary function of an organization that is directly involved in the production of goods or services. Line managers are responsible for the day-to-day operations of the organization and have authority over employees.

A matrix function is a hybrid of line and staff functions. In a matrix organization, employees report to both a line manager and a staff manager. This type of organization is often used in complex organizations with multiple projects or divisions.

A line and staff function is a function that is both a line function and a staff function. This type of function is often used in organizations with a large number of employees.