# How to Solve for the Maximization of Profit When a Given Relationship Is Between Profit & Output

by Kathy Adams McIntosh

Investors and lenders observe the profit earning power of each business when they read the financial statements published by each company. This helps them make investing and lending decisions. For each company, a profit maximization point exists. This point determines the sales quantity where the company experiences the highest profit per unit of output. Prior to reaching this point, the company pays fixed costs and variable costs from each unit sale, and earns a lower profit. After reaching this point, the company experiences an increase in fixed costs, which reduces the profit per unit.

1. Create a table. Label the first column “Output.” Label the second column “Total Cost.”

2. Enter various levels of output into the first column of the table. Enter the total cost the company would incur at each level of output in the second column.

3. Create a graph. Label the horizontal axis “Output.” Label the vertical axis “Total Cost.”

4. Plot each value from the table on the graph. Draw a line connecting the points on the graph. The highest point represents the profit maximizing output quantity.

#### Tips

• Other methods of solving for the profit maximization point include comparing the marginal revenue to marginal cost method or the maximizing revenue method. The data used in each method varies slightly. This method creates a visual picture for the user.
• Units sold beyond the profit maximization point will continue to generate revenue and profit for the company. However, the amount of profit will decline with each additional unit.
• This profit maximization point only applies while the costs and selling prices remain current. When the costs and selling prices change, the profit maximization point also changes and needs to be recalculated. If you use spreadsheet software with graphing capabilities, you can estimate the impact of price changes or cost increases. Update the numbers in your table and recreate the graph.
• Consider the selling capacity of your product along with the profit maximization point. If your product sales reaches its limit at a lower level of output, your company will not reach its profit maximization point.

#### Photo Credits

• Jack Hollingsworth/Digital Vision/Getty Images