he marginal cost for a product is MC = 3x + 20, and the fixed cost is $80.

Find the cost of producing 10 unit

To find the total cost of producing 10 units, we need to calculate both the variable cost (using the marginal cost function) and the fixed cost.

### Marginal cost function:
\[
MC = 3x + 20
\]
where $x$ represents the number of units produced. To find the variable cost, we integrate the marginal cost function with respect to $x$:

\[
C(x) = \int MC \, dx = \int (3x + 20) \, dx
\]
This gives:
\[
C(x) = \frac{3x^2}{2} + 20x + C_0
\]
where $C_0$ is the fixed cost, which is $80.

### Now, substitute $x = 10$ into the cost equation:

\[
C(10) = \frac{3(10)^2}{2} + 20(10) + 80
\]
\[
C(10) = \frac{3(100)}{2} + 200 + 80
\]
\[
C(10) = 150 + 200 + 80 = 430
\]

### Therefore, the total cost of producing 10 units is \$430.

Would you like further details, or do you have any questions?

Here are some related questions for practice:
1. What would be the cost of producing 15 units using the same marginal cost function?
2. How does the marginal cost impact total cost as the number of units increases?
3. How would the cost change if the fixed cost increased to \$100?
4. What is the total variable cost of producing 10 units, excluding the fixed cost?
5. How does integrating the marginal cost function help in finding total cost?

**Tip:** Integrating a marginal cost function gives the total cost function. Don't forget to account for fixed costs!

The marginal cost for a product is MC = 3x + 20, and the fixed cost is $80. Find the cost of producing 10 units.

Learn how to calculate the total cost of producing 10 units when the marginal cost function is MC = 3x + 20 and the fixed cost is $80. This detailed step-by-step solution explains integration of the marginal cost function and includes key concepts from algebra and calculus. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation