Final answer:
The question is about calculating a firm's profitability by analyzing its cost function and revenue function, with the example indicating how to determine profit when the cost and revenue for a specific quantity are known. The total revenue at a price of $16 per unit would be total revenue of $640, and if the total cost is $580, then the profit is $60.
Step-by-step explanation:
The subject of the question involves understanding the cost function C(x) and the revenue function R(x) of a firm and how these functions can be used to determine profitability. The cost function given is C(x) = 0.0001x³ - 0.012x² + 100x + 40,000, and the revenue function is R(x) = 350x. A firm must determine the quantity of output (x) that will maximize its profits, which is the difference between total revenue and total cost.
When analyzing profitability, the firm will look for the point where revenue exceeds cost. One way to find this is by setting R(x) greater than C(x) and solving for x. For example, if a firm produces 40 units, the total revenue at a price of $16 per unit would be total revenue of $640, and if the total cost is $580, then the profit is $60.
Understanding the concept of price multiplied by quantity is essential in this context because it provides the basis for calculating total revenue. Moreover, knowing that the firm's cost is the sum of all costs associated with production is key for analyzing total cost.