Final answer:
The Pear Company calculates profits by subtracting total costs from total revenues, utilizing the cost function C(x) and the revenue function R(x) for their Pphones. For a quantity of 40 Pphones at a price of $16, the firm can achieve a profit of $60. The goal is to produce at a quantity where this profit is maximized.
Step-by-step explanation:
The Pear Company engages in the manufacture of Pphones, factoring in the associated production costs and overheads into their cost function, which is represented as C(x) = -29x^2 + 66000x + 18331 dollars. To determine profitability, we must compare the revenue function, in this case given as R(x) = -34x^2 + 21600x dollars, with the cost function. When the Pear Company sells Pphones at their maximum price, they aim to set the price where their total revenue is maximized relative to their total costs. From the data provided, we understand that if the company were to sell 40 Pphones at a price of $16, they would make a profit. The total revenue at this output level is $640, and the total cost is $580, which results in a profit of $60. It's important to note that profit is calculated as total revenue minus total costs. To optimize profit, the Pear Company must produce and sell at a quantity where this difference is the greatest.
Through analysis of the revenue and cost functions, the Pear Company can establish the most profitable quantity of Pphones to produce. This ensures that the firm maximizes its economic profits and remains competitive in the market.