A Model Of The Total Cost $C$, In Dollars, To Produce $n$ Cell Phones Is Given By $C = 180n + 800$.(a) Find The $C$-intercept.\[$(n, C) = (\square)\$\]Write A Sentence To Explain The Meaning Of The Intercept

Introduction

In the world of business and economics, understanding the total cost of production is crucial for making informed decisions. A model of the total cost $C$, in dollars, to produce $n$ cell phones is given by the equation $C = 180n + 800$. In this article, we will delve into the world of mathematics and explore the concept of the $C$-intercept, which is a critical point in the total cost model.

What is the $C$-Intercept?

The $C$-intercept is a point on the total cost graph where the number of cell phones produced is zero, and the total cost is at its maximum. In other words, it is the point where the total cost is not affected by the number of cell phones produced.

Finding the $C$-Intercept

To find the $C$-intercept, we need to substitute $n = 0$ into the total cost equation. This will give us the total cost when no cell phones are produced.

C = 180(0) + 800
C = 800

Therefore, the $C$-intercept is $(0, 800)$.

Interpretation of the $C$-Intercept

The $C$-intercept represents the fixed cost of producing cell phones, which is $800 in this case. This means that even if no cell phones are produced, the company still incurs a cost of $800. This cost can be attributed to the initial investment in the production process, such as setting up the factory, purchasing equipment, and hiring staff.

Discussion

The $C$-intercept is an important concept in the total cost model, as it provides valuable insights into the fixed costs associated with producing cell phones. By understanding the $C$-intercept, businesses can make informed decisions about their production levels and pricing strategies.

Conclusion

In conclusion, the $C$-intercept is a critical point in the total cost model, representing the fixed cost of producing cell phones. By finding the $C$-intercept, businesses can gain a deeper understanding of their production costs and make informed decisions about their operations.

Total Cost Model

The total cost model is given by the equation $C = 180n + 800$. This equation represents the total cost of producing $n$ cell phones.

Graph of the Total Cost Model

The graph of the total cost model is a straight line with a positive slope. The $C$-intercept is the point where the line intersects the $y$-axis.

Key Takeaways

• The $C$-intercept is a critical point in the total cost model, representing the fixed cost of producing cell phones.
• The $C$-intercept is found by substituting $n = 0$ into the total cost equation.
• The $C$-intercept represents the initial investment in the production process, such as setting up the factory, purchasing equipment, and hiring staff.

Real-World Applications

The total cost model has numerous real-world applications in business and economics. For example, it can be used to:

• Determine the optimal production level to minimize costs
• Set prices for products based on production costs
• Make informed decisions about investments in new equipment or technology

Conclusion

$$$$

Introduction

In our previous article, we explored the concept of the total cost model and the $C$-intercept. In this article, we will answer some frequently asked questions about the total cost model and the $C$-intercept.

Q: What is the total cost model?

A: The total cost model is a mathematical equation that represents the total cost of producing a certain number of cell phones. The equation is given by $C = 180n + 800$, where $C$ is the total cost and $n$ is the number of cell phones produced.

Q: What is the $C$-intercept?

A: The $C$-intercept is a point on the total cost graph where the number of cell phones produced is zero, and the total cost is at its maximum. It represents the fixed cost of producing cell phones.

Q: How do I find the $C$-intercept?

A: To find the $C$-intercept, you need to substitute $n = 0$ into the total cost equation. This will give you the total cost when no cell phones are produced.

Q: What does the $C$-intercept represent?

A: The $C$-intercept represents the initial investment in the production process, such as setting up the factory, purchasing equipment, and hiring staff.

Q: How can I use the total cost model in real-world applications?

A: The total cost model can be used to determine the optimal production level to minimize costs, set prices for products based on production costs, and make informed decisions about investments in new equipment or technology.

Q: What are some common mistakes to avoid when working with the total cost model?

A: Some common mistakes to avoid when working with the total cost model include:

• Not considering the fixed costs associated with producing cell phones
• Not accounting for the variable costs associated with producing cell phones
• Not using the correct equation to represent the total cost model

Q: How can I graph the total cost model?

A: The graph of the total cost model is a straight line with a positive slope. The $C$-intercept is the point where the line intersects the $y$-axis.

Q: What are some real-world examples of the total cost model?

A: Some real-world examples of the total cost model include:

• A company that produces cell phones and wants to determine the optimal production level to minimize costs
• A retailer that wants to set prices for cell phones based on production costs
• A manufacturer that wants to make informed decisions about investments in new equipment or technology

Conclusion

In conclusion, the total cost model and the $C$-intercept are critical concepts in business and economics. By understanding the total cost model and the $C$-intercept, businesses can make informed decisions about their production levels and pricing strategies.

Frequently Asked Questions

• Q: What is the total cost model?
• A: The total cost model is a mathematical equation that represents the total cost of producing a certain number of cell phones.
• Q: What is the $C$-intercept?
• A: The $C$-intercept is a point on the total cost graph where the number of cell phones produced is zero, and the total cost is at its maximum.
• Q: How do I find the $C$-intercept?
• A: To find the $C$-intercept, you need to substitute $n = 0$ into the total cost equation.

Glossary

• Total cost model: A mathematical equation that represents the total cost of producing a certain number of cell phones.
• $C$-intercept: A point on the total cost graph where the number of cell phones produced is zero, and the total cost is at its maximum.
• Fixed cost: The initial investment in the production process, such as setting up the factory, purchasing equipment, and hiring staff.
• Variable cost: The cost associated with producing a certain number of cell phones, such as the cost of raw materials and labor.