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Let's break down the information given in the problem:

- The fixed costs are \$15,640.
- The variable cost per DVD is \$8.45.
- The selling price per DVD is \$19.95.

### (A) Finding the Cost Equation:
The total cost $C(x)$ is made up of two parts:
1. **Fixed costs**: These remain constant, no matter how many DVDs are sold. This is \$15,640.
2. **Variable costs**: These depend on the number of DVDs produced. For each DVD, the variable cost is \$8.45. So, for $x$ DVDs, the variable cost is $8.45x$.

Thus, the **cost equation** is:
\[
C(x) = 15640 + 8.45x
\]

Would you like further details on the cost equation, or should we proceed to part (B) of the problem? Here are some questions to further your understanding:

1. What is the meaning of fixed costs in a cost equation?
2. How does the variable cost affect the total cost when more DVDs are sold?
3. How would the cost equation change if the variable cost per DVD was increased?
4. Can you find the cost of producing 100 DVDs using the cost equation?
5. Why is it important to separate fixed and variable costs in business models?

**Tip:** Always verify if fixed costs are truly constant across production volumes before applying them in business models.

A company markets exercise DVDs that sell for $19.95, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $15,640, and the variable costs (materials, shipping, etc.) are $8.45 per DVD. (A) Find the cost equation and the revenue equation. (B) How many DVDs must be sold each month for the company to break even? (C) Graph the cost and revenue equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.

Learn how to find the cost and revenue equations for a company selling DVDs at $19.95 each, with monthly fixed costs of $15,640 and a variable cost of $8.45 per DVD. This problem involves algebraic concepts like linear equations and break-even analysis. Suitable for students in Grades 9-12.

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