https://file.aiquickdraw.com/mathbot/file/1729715881523t9n53thx.jpg

We are given the following functions:

- **Revenue function**: $ R(x) = 19x $
- **Cost function**: $ C(x) = 7x + 1116 $

### Step 1: Find the Profit Function
The profit function $ P(x) $ is defined as the difference between the revenue and cost:

\[
P(x) = R(x) - C(x)
\]

Substituting the given expressions:

\[
P(x) = 19x - (7x + 1116)
\]
Simplifying this:

\[
P(x) = 19x - 7x - 1116
\]
\[
P(x) = 12x - 1116
\]

### Step 2: Find the value of $ x $ that gives a profit of $1620
We are asked to find how many units $ x $ must be produced to get a profit of 1620. Set $ P(x) = 1620 $:

\[
1620 = 12x - 1116
\]
Now, solve for $ x $:

\[
1620 + 1116 = 12x
\]
\[
2736 = 12x
\]
\[
x = \frac{2736}{12}
\]
\[
x = 228
\]

### Final Answer:
The business must produce **228 units** to make a profit of $1620.

Would you like more details or have any questions about this process?

Here are some additional questions to consider:
1. What happens if the fixed cost increases in the cost function?
2. How would a change in the selling price affect the revenue function?
3. Can you interpret the breakeven point using these functions?
4. How would the profit change if the number of units doubled?
5. What if the profit required was higher, say $2000?

**Tip**: In general, the profit function is always revenue minus cost. Always remember this structure when solving similar problems.

The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to make a profit of $1620.

Learn how to calculate profit using linear revenue and cost functions. This example solves for the number of units needed to achieve a profit of $1620. Ideal for students in Grades 9-11 studying linear functions and profit equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation