Final answer:
If the center's variable costs exceed its revenues, it is not covering costs that can be avoided by shutting down, leading to the recommendation that the center should shut down immediately.
Step-by-step explanation:
When assessing the financial situation of a business, especially regarding closure decisions, a key consideration is whether the revenues cover the variable costs. In the given scenario, the center earns revenues of $10,000, but the variable costs are higher, amounting to $15,000. This signifies a loss of $5,000, which is essentially the amount by which the costs exceed the revenues.
Typically, in the short term, if a company is not able to cover its variable costs, it may be better to shut down operations immediately because it indicates that the company is not even covering the costs it can avoid by not operating. Each additional unit of production or service will add to the overall loss. In contrast, if revenues were at least equal to variable costs, the company could continue operating in the short term as long as the additional revenue from each unit sold covers the variable cost of producing that unit, contributing something towards fixed costs and potential eventual profits. However, the loss incurred when variable costs exceed revenues cannot be justified as no contribution is made to fixed costs or profit.