Final answer:
The correct answer is a profit center, where managers are accountable for both revenues and expenses. Examples given show a profit center earning revenues of $20,000 with variable costs of $15,000 should continue, while one with reversed figures may need to shut down.
Step-by-step explanation:
A responsibility center in which managers are held accountable for both revenues and expenses is referred to as a profit center. This type of center is responsible for generating income as well as managing costs to produce a profit. For instance, if a center earns revenues of $20,000 and has variable costs of $15,000, it is contributing positively to the organization's profit by generating a surplus of $5,000 and should continue in business.
On the other hand, if a center reports revenues of $10,000 with variable costs of $15,000, it is not contributing to profit and is instead running at a loss of $5,000. In this scenario, the center is not covering its variable costs through earned revenues and may warrant consideration for closure unless there are strategic reasons for maintaining its operations.