A manager, who is responsible for both cost and revenues belongs to department of

cost center
revenue center
profit center
investment center

The correct answer is C. profit center.

A cost center is a department or division of a company that incurs costs but does not directly generate revenue. Examples of cost centers include accounting, human resources, and IT.

A revenue center is a department or division of a company that generates revenue but does not directly incur costs. Examples of revenue centers include sales and marketing.

A profit center is a department or division of a company that incurs costs and generates revenue. The manager of a profit center is responsible for both costs and revenues, and is therefore accountable for the profit or loss of the department.

An investment center is a department or division of a company that incurs costs, generates revenue, and has control over its own assets. The manager of an investment center is responsible for all three of these factors, and is therefore accountable for the return on investment (ROI) of the department.

In conclusion, the correct answer is C. profit center.