Select The Correct Answer.A Mobile Virtual Reality (VR) Headset Is Being Sold At A Local Department Store For $\$33.75$. This Is The Cost Function Associated With The Headsets, Where $x$ Represents The Number Of Headsets Manufactured

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Introduction

In the world of economics and business, understanding the cost function is crucial for making informed decisions about production and pricing. A cost function is a mathematical representation of the total cost of producing a certain quantity of a product. In this article, we will explore the cost function associated with a mobile virtual reality (VR) headset and learn how to select the correct answer.

The Cost Function

The cost function associated with the mobile VR headset is given by the equation:

C(x)=33.75xC(x) = 33.75x

where C(x)C(x) represents the total cost of producing xx headsets, and xx represents the number of headsets manufactured.

Understanding the Cost Function

To understand the cost function, let's break it down into its components. The cost function is a linear function, which means that it has a constant rate of change. In this case, the rate of change is $33.75, which represents the cost of producing one headset.

Interpreting the Cost Function

The cost function can be interpreted in several ways:

  • Fixed Cost: The cost function has a fixed cost of $0, which means that there are no fixed costs associated with producing the headsets.
  • Variable Cost: The cost function has a variable cost of $33.75, which means that the cost of producing one headset is $33.75.
  • Total Cost: The cost function represents the total cost of producing xx headsets, which is given by the equation C(x)=33.75xC(x) = 33.75x.

Selecting the Correct Answer

Now that we have understood the cost function, let's select the correct answer. The question states that the mobile VR headset is being sold at a local department store for $33.75\$33.75. This is the cost function associated with the headsets, where xx represents the number of headsets manufactured.

To select the correct answer, we need to determine the value of xx that corresponds to the given cost of $33.75\$33.75. We can do this by setting up an equation using the cost function:

33.75x=33.7533.75x = 33.75

Solving for xx, we get:

x=1x = 1

Therefore, the correct answer is that the mobile VR headset is being sold at a local department store for $33.75\$33.75 when x=1x = 1.

Conclusion

In conclusion, understanding the cost function is crucial for making informed decisions about production and pricing. The cost function associated with the mobile VR headset is given by the equation C(x)=33.75xC(x) = 33.75x, where C(x)C(x) represents the total cost of producing xx headsets, and xx represents the number of headsets manufactured. By interpreting the cost function, we can determine the value of xx that corresponds to the given cost of $33.75\$33.75, which is x=1x = 1.

Additional Examples

To further illustrate the concept of the cost function, let's consider a few additional examples:

  • Example 1: Suppose the cost function associated with the mobile VR headset is given by the equation C(x)=25x+10C(x) = 25x + 10. What is the value of xx that corresponds to the given cost of $35\$35?
  • Example 2: Suppose the cost function associated with the mobile VR headset is given by the equation C(x)=20x−5C(x) = 20x - 5. What is the value of xx that corresponds to the given cost of $30\$30?

Solving the Examples

To solve the examples, we can use the same approach as before. We can set up an equation using the cost function and solve for xx.

  • Example 1: Setting up the equation, we get:

25x+10=3525x + 10 = 35

Solving for xx, we get:

x=1x = 1

Therefore, the value of xx that corresponds to the given cost of $35\$35 is x=1x = 1.

  • Example 2: Setting up the equation, we get:

20x−5=3020x - 5 = 30

Solving for xx, we get:

x=2x = 2

Therefore, the value of xx that corresponds to the given cost of $30\$30 is x=2x = 2.

Conclusion

Q: What is the cost function, and how is it used in economics and business?

A: The cost function is a mathematical representation of the total cost of producing a certain quantity of a product. It is used in economics and business to determine the cost of producing a product, and to make informed decisions about production and pricing.

Q: What is the cost function associated with the mobile VR headset?

A: The cost function associated with the mobile VR headset is given by the equation C(x)=33.75xC(x) = 33.75x, where C(x)C(x) represents the total cost of producing xx headsets, and xx represents the number of headsets manufactured.

Q: How do I interpret the cost function?

A: To interpret the cost function, you need to understand the components of the function. The cost function is a linear function, which means that it has a constant rate of change. In this case, the rate of change is $33.75, which represents the cost of producing one headset.

Q: What are the fixed and variable costs associated with the mobile VR headset?

A: The cost function has a fixed cost of $0, which means that there are no fixed costs associated with producing the headsets. The variable cost is $33.75, which means that the cost of producing one headset is $33.75.

Q: How do I determine the value of x that corresponds to a given cost?

A: To determine the value of xx that corresponds to a given cost, you need to set up an equation using the cost function and solve for xx. For example, if the given cost is $33.75\$33.75, you can set up the equation 33.75x=33.7533.75x = 33.75 and solve for xx.

Q: What are some additional examples of cost functions?

A: Some additional examples of cost functions include:

  • C(x)=25x+10C(x) = 25x + 10
  • C(x)=20x−5C(x) = 20x - 5
  • C(x)=15x+20C(x) = 15x + 20

Q: How do I solve for x in a cost function?

A: To solve for xx in a cost function, you need to set up an equation using the cost function and solve for xx. For example, if the cost function is C(x)=25x+10C(x) = 25x + 10 and the given cost is $35\$35, you can set up the equation 25x+10=3525x + 10 = 35 and solve for xx.

Q: What is the importance of understanding the cost function in economics and business?

A: Understanding the cost function is crucial in economics and business because it allows you to make informed decisions about production and pricing. By understanding the cost function, you can determine the cost of producing a product, and make decisions about how to allocate resources.

Q: Can you provide some real-world examples of cost functions?

A: Yes, here are some real-world examples of cost functions:

  • The cost function for a company that produces smartphones may be C(x)=200x+1000C(x) = 200x + 1000, where xx represents the number of smartphones produced.
  • The cost function for a company that produces computers may be C(x)=300x+500C(x) = 300x + 500, where xx represents the number of computers produced.
  • The cost function for a company that produces video games may be C(x)=100x+2000C(x) = 100x + 2000, where xx represents the number of video games produced.

Conclusion

In conclusion, understanding the cost function is crucial in economics and business. By understanding the cost function, you can make informed decisions about production and pricing. The cost function associated with the mobile VR headset is given by the equation C(x)=33.75xC(x) = 33.75x, where C(x)C(x) represents the total cost of producing xx headsets, and xx represents the number of headsets manufactured. By interpreting the cost function, you can determine the value of xx that corresponds to a given cost.