# Optimizing Business Functions

In earlier sections, we utilized revenue, cost, and profit functions to help us understand the ideas behind marginal functions. In this section we examine the graphs of these functions to help us make decisions about production levels for a business.

A business’s total revenue is the total amount of money received for selling a good or service. In general, the letters *TR* is used to name the total revenue function. It can be a function of any number of variables, but in this section we’ll think of the revenue function as being a function of the number of units of a product or service produced and sold, *Q*, or the unit price of a product or service, *P*.

The total cost a business incurs is the cost of all inputs the business uses in production. Some of these costs are fixed and others are variable. By this, we mean that as production changes, some costs change and others remain the same. The costs that change as the production changes are the variable costs.

Labor, the cost of materials and the cost of utilities are all examples of variable costs. The costs that are constant as the production changes are the fixed costs. Lease payments for a factory and retail space or payments for fire insurance are examples of fixed costs. Since all of a business’s costs are variable or fixed, the total cost is the sum of the fixed and variable costs:

Total Costs = Variable Costs + Fixed Costs

In general, the name *TC* is used to represent the total cost function. In this section, we assume that the total cost is a function of a single variable representing the number of units of a product or service produced and sold, *Q*, or the unit price of a product or service produced, *P*.

The profit for a business is the difference between the total revenue and the total cost,

Profit = Total Revenue – Total Costs

The letters *Pr* are used to denote the profit function. Don’t confuse *Pr* with *P*. Remember, *P* corresponds to the unit price of a good or service.

**Read**

- How do you maximize the revenue or profit for a business?
- How do you minimize the average cost for a business?
- Handout: Maximize Revenue Example
- Handout: Maximize Profit Example

- Handout: Minimize Average Cost Example

Section 12.3 Workbook (PDF) – 9/5/19

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