A Small-order Coffee Company Charges $12 For Each Bag Of Coffee Plus $3 Shipping, Regardless Of How Many Bags Are Ordered.Tasks:1. Describe A Function That Represents This Situation.2. Make A Table For This Function.3. Sketch A Graph Of This

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Introduction

In this article, we will explore a real-world scenario involving a small-order coffee company that charges a fixed price for each bag of coffee, plus a shipping fee, regardless of the number of bags ordered. We will create a mathematical function to represent this situation, generate a table to illustrate the function's behavior, and sketch a graph to visualize the cost.

Step 1: Describing the Function

Let's denote the number of bags of coffee ordered as x and the total cost as C(x). The company charges $12 for each bag of coffee, so the cost of x bags is 12x. Additionally, there is a fixed shipping fee of $3, regardless of the number of bags ordered. Therefore, the total cost function can be represented as:

C(x) = 12x + 3

This function describes the cost of ordering x bags of coffee, including the fixed shipping fee.

Step 2: Creating a Table for the Function

To better understand the behavior of the cost function, let's create a table with some sample values of x and the corresponding values of C(x).

x (Number of Bags) C(x) (Total Cost)
0 3
1 15
2 27
3 39
4 51
5 63

As we can see from the table, the cost increases linearly with the number of bags ordered, with a fixed shipping fee of $3 added to the total cost.

Step 3: Sketching a Graph of the Function

To visualize the cost function, let's sketch a graph of C(x) = 12x + 3.

**Graph of C(x) = 12x + 3**

    

  • The graph is a straight line with a positive slope of 12.
    • 

  • The y-intercept is 3, representing the fixed shipping fee.
    • 

  • As x increases, the graph rises linearly, representing the increasing cost of ordering more bags of coffee.

Here's a simple graph representation using ASCII art:

  y
  |
  | 3
  | 15
  | 27
  | 39
  | 51
  | 63
  v
  x

Conclusion

In this article, we created a mathematical function to represent the cost of ordering coffee from a small-order coffee company. We generated a table to illustrate the function's behavior and sketched a graph to visualize the cost. The cost function is a linear function with a positive slope of 12 and a y-intercept of 3, representing the fixed shipping fee. This model can be used to calculate the total cost of ordering coffee from the company.

Discussion

  • What are some potential applications of this cost function in real-world scenarios?
  • How might the company adjust its pricing strategy to optimize revenue?
  • What are some potential limitations of this model, and how might they be addressed?

Additional Resources

References

Introduction

In our previous article, we explored a real-world scenario involving a small-order coffee company that charges a fixed price for each bag of coffee, plus a shipping fee, regardless of the number of bags ordered. We created a mathematical function to represent this situation, generated a table to illustrate the function's behavior, and sketched a graph to visualize the cost. In this article, we will answer some frequently asked questions (FAQs) related to this scenario.

Q&A

Q1: What is the cost of ordering 0 bags of coffee?

A1: According to the cost function C(x) = 12x + 3, when x = 0, the cost is C(0) = 12(0) + 3 = 3. This represents the fixed shipping fee of $3.

Q2: How much does it cost to order 1 bag of coffee?

A2: Using the cost function, when x = 1, the cost is C(1) = 12(1) + 3 = 15. This represents the cost of 1 bag of coffee plus the fixed shipping fee of $3.

Q3: What is the slope of the cost function?

A3: The slope of the cost function is 12, which represents the rate at which the cost increases with the number of bags ordered.

Q4: What is the y-intercept of the cost function?

A4: The y-intercept of the cost function is 3, which represents the fixed shipping fee.

Q5: Is the cost function linear?

A5: Yes, the cost function is a linear function, which means it can be represented by a straight line.

Q6: Can the cost function be used to calculate the cost of ordering more than 5 bags of coffee?

A6: Yes, the cost function can be used to calculate the cost of ordering any number of bags of coffee, not just up to 5 bags.

Q7: How might the company adjust its pricing strategy to optimize revenue?

A7: The company might consider adjusting its pricing strategy by increasing the cost per bag of coffee or by offering discounts for larger orders.

Q8: What are some potential limitations of this model?

A8: Some potential limitations of this model include:

  • The model assumes a fixed shipping fee, which may not be the case in reality.
  • The model does not take into account other costs, such as labor or overhead costs.
  • The model assumes that the cost per bag of coffee remains constant, which may not be the case in reality.

Conclusion

In this article, we answered some frequently asked questions related to the small-order coffee company scenario. We hope this Q&A article has provided additional insight and clarity on the cost function and its applications.

Discussion

  • What are some potential applications of this cost function in real-world scenarios?
  • How might the company adjust its pricing strategy to optimize revenue?
  • What are some potential limitations of this model, and how might they be addressed?

Additional Resources

References