Find the profit function P(x) determined by the given cost and revenue functions. (See Example 6.)
R(x)	 = 	21x
C(x)	 = 	13x + 58
P(x) =	 


To find the profit function \( P(x) \), we use the relationship:

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

where:
- \( R(x) \) is the revenue function
- \( C(x) \) is the cost function

Given:
\[
R(x) = 21x, \quad C(x) = 13x + 58
\]

Substitute these into the formula for \( P(x) \):

\[
P(x) = 21x - (13x + 58)
\]

Simplify the expression:

\[
P(x) = 21x - 13x - 58
\]

\[
P(x) = 8x - 58
\]

So, the profit function is:

\[
\boxed{P(x) = 8x - 58}
\]

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

### Related Questions:
1. How do you determine the break-even point using the profit function?
2. What does the coefficient of \( x \) in the profit function represent?
3. How would a change in the cost function affect the profit function?
4. If \( R(x) = 25x \) and \( C(x) = 15x + 100 \), what is the profit function?
5. What is the meaning of the constant term in the profit function?

### Tip:
The profit function shows how much profit is made for each unit sold, minus any fixed costs.

Find the profit function P(x) determined by the given cost and revenue functions. R(x) = 21x, C(x) = 13x + 58.

Learn how to determine the profit function P(x) from given revenue and cost functions: R(x) = 21x and C(x) = 13x + 58. This step-by-step algebraic solution simplifies P(x) and shows how profit depends on sales volume. Suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation