Final answer:
To maximize profits, calculate total revenue and total cost at each output level, then determine where profit, the difference between them, is largest.
A table can help identify the output level with the highest profit without using calculus.
Step-by-step explanation:
Calculating Profit Maximization
To calculate the quantity of output that will provide the highest level of profit, we begin by comparing the total revenue (TR) and total cost (TC) for each level of output (q).
Profits (π) are determined by subtracting total costs from total revenues (π = TR - TC). The goal is to find the output level where profit is maximized, which is the largest vertical gap between the TR and TC curves.
Given the total cost function TC = 1q³ - 40q² + 840q + 1800 and a fixed price of $750 per unit, we first calculate the total revenue, which is TR = $750 * q. We then calculate profit by subtracting the TC from the TR for various quantities.
The process involves constructing a table with each output level (usually in integer units), calculating corresponding TR, TC, and profit, and then locating the largest profit number. This will represent the optimal level of production.
Example: If we assume a quantity of 60 units, TR is calculated as $750 * 60 = $45,000. Using the TC function, TC at 60 units will be 1 * 60³ - 40 * 60² + 840 * 60 + 1800.
Profit is then found by subtracting this TC from the TR. We follow this process for a range of quantities to determine where profit peaks.