Final answer:
An Investment center (option c) is the responsibility center that considers investments using a common cost of capital percentage and includes evaluation based on ROI; this type of center has decision-making authority over investment, expenses, and revenues.
Step-by-step explanation:
The responsibility center structure that considers investments made by the operating segments by using a common cost of capital percentage is called an Investment center. Unlike a Cost center, which only emphasizes minimizing costs, or a Revenue center, which is focused on revenue generation without regard to the costs of achieving that revenue, an Investment center involves assessing both revenues and costs, and in addition, its performance is evaluated based on its return on investment (ROI).
Management of an Investment center has the autonomy not only to make decisions about expenses and revenues but also about the investments made in fixed assets and working capital.
Given the scenario where the center earns revenues of $20,000, and variable costs are $15,000, the center's current operations suggest it is generating a gross profit or contribution margin, which indicates that the center should continue in business, at least from the short-term perspective where fixed costs and investment returns are not specified.