The concept that helps the Human Resource Manager in deciding the actual number of personnel required in each department is typically referred to as "Workforce Planning" or "Human Resource Planning."
Workforce Planning involves assessing the current and future workforce needs of an organization to ensure that it has the right number of employees with the right skills at the right time. In the context you described, as the demand for the product grew, the Human Resource Manager would engage in workforce planning to determine how many additional employees are needed in each department (production, marketing, finance, and human resources) to meet the increased demand effectively.
This process may involve analyzing current workforce capabilities, forecasting future demand, identifying skill gaps, and developing strategies to address these gaps. The goal is to align the workforce with the organizational objectives and ensure that the company has the necessary talent to achieve its goals.