Final answer:
The two branches of classical management are scientific management, which focuses on labor productivity and efficiency, and administrative management, which focuses on the organization's structure and management principles.
Step-by-step explanation:
The two branches of the classical viewpoint of management as mentioned in the question are scientific management and administrative management. Scientific management is a theory that analyzes and synthesizes workflows, primarily concerned with improving economic efficiency and labor productivity. Its main proponent, Frederick Taylor, focused on the optimization of work through techniques such as time-and-motion studies and standardized tools and procedures.
On the other hand, administrative management concentrates on the organization and its structure, management principles, and the functions of management. Henri Fayol is known for his contribution to this branch, emphasizing the management process' and principles' universality. He introduced concepts such as division of work, unity of command, and the scalar chain.
These two viewpoints have shaped the evolution of management theory and still influence managerial practices in various organizations today.