A segment of a business responsible for both revenues and expenses would be called:

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A profit centre is a segment of a business responsible for generating and incurring both revenues and expenses. It is evaluated based on its ability to earn profits and its contribution to the overall success of the business. A cost centre is a segment responsible for incurring expenses but not directly generating revenue, while an investment centre is responsible for both generating revenue and managing investments. There is no such thing as a motivation centre in accounting or finance.

A Segment of a Business Responsible for Both Revenues and Expenses