Final answer:
The 'administration' function is typically associated with supporting value-chain analysis in a business context. The reference question, however, addresses functionalism's view of government purposes, which includes 'planning and directing society' as one of its main functions. Therefore, the correct answer from the options provided would be 'administration'.
Step-by-step explanation:
The function that supports the six functions of value-chain analysis is often considered to be part of the management process in business. However, the student's question seems to be mixing topics, so based on the provided information and reference question, the correct function that supports value-chain analysis would-be administration. The four main purposes of government in functionalism, which do not include value-chain analysis, are maintaining law and order, meeting social needs, equally distributing resources, and planning and directing society. Regarding the reference question, the correct answer is that 'Planning and directing society' is one of the four main purposes of functionalism's view of government, so the answer to the student's question about the function that supports value-chain analysis would not align with the options provided. In the context of value-chain analysis, administration is critical as it encompasses organizing, staffing, and operations management, which support the primary and support activities within the value chain.