### Learning Outcomes

- Write polynomials involving cost, revenue, and profit

In this section, we will see that polynomials are sometimes used to describe cost and revenue.

Profit is typically defined in business as the difference between the amount of money earned (revenue) by producing a certain number of items and the amount of money it takes to produce that number of items. When you are in business, you definitely want to see profit, so it is important to know what your cost and revenue is.

For example, let’s say that the cost to a manufacturer to produce a certain number of things is C and the revenue generated by selling those things is R. The profit, P, can then be defined as

P = R-C

The example we will work with is a hypothetical cell phone manufacturer whose cost to manufacture x number of phones is [latex]C=2000x+750,000[/latex], and the Revenue generated from manufacturing x number of cell phones is [latex]R=-0.09x^2+7000x[/latex].

### Example

Define a Profit polynomial for the hypothetical cell phone manufacturer.

Mathematical models are great when you use them to learn important information. The cell phone manufacturing company can use the profit equation to find out how much profit they will make given x number of phones are manufactured. In the next example, we will explore some profit values for this company.

### Example

Given the following numbers of cell phones manufactured, find the profit for the cell phone manufacturer:

- x = [latex]100[/latex] phones
- x = [latex]25,000[/latex] phones
- x= [latex]60,000[/latex] phones

Interpret your results.

### Try It

In the video that follows, we present another example of finding a polynomial profit equation.

We have shown that profit can be modeled with a polynomial, and that the profit a company can make based on a business model like this has its bounds.