Final answer:
The question involves using a profit function to calculate profit or loss at varying production levels. It explains how total revenues and total costs determine the firm's profitability, and identifies profit maximizing levels by exemplifying the process with specific quantities and prices.
Step-by-step explanation:
The student's question relates to a profit function and how it can be used to determine the profit or loss at a certain level of quantity and output in a business scenario. In this particular case, the profit function P(x) = -0.05x² + 85x - 10 calculates the profit in thousands of dollars for producing x units. For instance, if we consider producing five units, where each unit is sold at $25, the total revenues would be $125. However, if the total costs when producing these units is $130, the firm would experience a loss of $5. This illustrates how a firm can use the profit function to assess its financial situation.
Furthermore, the firm can determine the profit-maximizing output level, which is the quantity that yields the highest profit. For example, if at an output quantity of 5, the firm realizes profits of $40 (not accounting for the loss mentioned earlier), this could represent a profitable operation. Additionally, at an output of 40 units and a chosen price of $16 per unit, with an average cost of $14.50, the firm would make economic profits amounting to $60, because the total revenue ($640) exceeds the total cost ($580).