Final answer:
The maximum output attainable for a total cost of $20,000 cannot be determined without additional information on the firm's cost structure and production function. The profit-maximizing output level is where total revenue exceeds total costs by the largest amount.
Step-by-step explanation:
If a firm is minimizing cost to produce 270 units of output for $20,000, we would need additional information to determine the maximum output attainable for the same cost. However, when a firm moves to maximize output with a constrained total cost, it will adjust the combination of inputs and possibly the production technology to achieve this. Given that the provided information does not specify the prevailing costs of inputs or technology used, we cannot accurately determine the maximum output. To find it, we would need data on the cost structure of the firm, including variable and fixed costs, and the production function that relates input to output quantities.
The profit-maximizing output level occurs when the difference between total revenue and total costs is greatest. This can be observed by analyzing the point where the vertical gap between total revenue and total cost curves is at its maximum. In the examples given, losses are incurred when total costs exceed total revenues, and profits are made when total revenues are above total costs. The specifics of output quantity related to cost minimization or maximization could be illustrated numerically with complete data.