**Learning Objectives**

In this section, you will:

- Draw a picture of the scenario a word problem describes.
- Define all the variables mentioned in a word problem.
- Analyze word problems for “buzz” words and translate them into mathematical notation.
- Define the objective function described in a word problem.
- Define constraint functions and use them to make the objective function of one variable.

**Let’s Get Started Talking About Applied Optimization**

We have used derivatives to help find the maximums and minimums of some functions given by equations, but it is very unlikely that someone will simply hand you a function and ask you to find its extreme values. More typically, someone will describe a problem and ask your help in maximizing or minimizing something: What is the largest volume package which the post office will take?

; What is the quickest way to get from here to there?

; or What is the least expensive way to accomplish some task?

In this section, we’ll discuss how to find these extreme values using calculus.

In business applications, we are often interested to maximize revenue, or maximize profit and minimize costs. For example, we can determine the derivative of the profit function and use this analysis to determine conditions to maximize profit levels for a business.