It is our historical experience that all organizations created by humans undergo rise and fall. The historian Toynbee explained the rise and fall throughout history through the concepts of "challenge" and "response," and this theory has gained solid support in historiography. For the application of the Toynbee hypothesis as a management theory to explain the rise and fall of enterprises, the concepts of challenge and response must be uniquely defined in management terms. In this paper, the survival condition of a firm is expressed as a single inequality, which we call the firm's "survival inequality." If we view the threats of environmental change that can destroy the survival inequality as challenges, and the firm's efforts to continuously maintain it as responses, then the conclusion of this paper is that Toynbee's historical theory can be applied to business administration. This paper defines the entity responsible for maintaining the survival inequality and making decisions as the manager, and defines the manager's mission as the recognition of continuous challenges and successful responses to them. The content of this paper is an attempt to establish a general theory of business administration that transcends the level of fragmentary techniques through an interdisciplinary approach, using this framework of thought.