Answer:
I and III are correct.
Step-by-step explanation:
The first option is correct because a profit center is a subunit in a company in charge of all the sales operation, it controls the costs of production, sales, and revenue.
A cost center focuses on control costs and costs reduction. It does help to increase the company's profits, because the lower the costs, the greater the profit; but it doesn't directly interfere with any sales operation.