Final answer:
The function of a manager that involves deciding staff placement and task assignments in a healthcare setting is known as organizing and staffing.
Step-by-step explanation:
Deciding which staff are most appropriate to work on a specific patient care unit and assigning them work tasks would best be described as the key function of a manager known as organizing and staffing. This involves determining the structure of the team or organization, what roles are needed, and matching the right people to the right roles based on their skills, experience, and qualifications. The aim of organizing and staffing is to create an efficient workplace with capable employees who can meet the organization's objectives.