A Company Produces Microwaves. The Cost Of Producing $x$ Microwaves Per Month Is Given By$C(x) = 5,000 + 50x - 0.25x^2$What Is The Marginal Cost At A Production Level Of 150 Microwaves Per Month? Give Your Answer As An Integer. Do Not

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Evaluating Marginal Cost in Microwave Production

In the world of economics and business, understanding the cost of production is crucial for making informed decisions. The cost of producing a certain quantity of goods or services can be represented by a function, known as the cost function. In this article, we will explore the concept of marginal cost and how it can be evaluated using the given cost function for microwave production.

Marginal Cost and Its Importance

Marginal cost is the additional cost incurred by producing one more unit of a good or service. It is a measure of the rate of change of the total cost with respect to the quantity produced. In other words, it represents the change in the total cost when the production level is increased by one unit. Marginal cost is an essential concept in economics and business as it helps in determining the optimal production level.

The Cost Function

The cost function for producing microwaves is given by:

C(x)=5,000+50x−0.25x2C(x) = 5,000 + 50x - 0.25x^2

where xx represents the number of microwaves produced per month.

Evaluating Marginal Cost

To evaluate the marginal cost at a production level of 150 microwaves per month, we need to find the derivative of the cost function with respect to xx. The derivative of the cost function represents the rate of change of the total cost with respect to the quantity produced, which is the marginal cost.

Using the power rule of differentiation, we can find the derivative of the cost function as follows:

C′(x)=ddx(5,000+50x−0.25x2)C'(x) = \frac{d}{dx} (5,000 + 50x - 0.25x^2)

C′(x)=50−0.5xC'(x) = 50 - 0.5x

Now, we can evaluate the marginal cost at a production level of 150 microwaves per month by substituting x=150x = 150 into the derivative:

C′(150)=50−0.5(150)C'(150) = 50 - 0.5(150)

C′(150)=50−75C'(150) = 50 - 75

C′(150)=−25C'(150) = -25

Interpretation of Results

The marginal cost at a production level of 150 microwaves per month is −25-25. This means that if the company produces one more unit of microwave, the total cost will decrease by $25.

In conclusion, we have evaluated the marginal cost at a production level of 150 microwaves per month using the given cost function. The marginal cost represents the rate of change of the total cost with respect to the quantity produced, which is essential for making informed decisions in business and economics.

Limitations and Future Work

While this article has provided a comprehensive analysis of the marginal cost at a production level of 150 microwaves per month, there are several limitations and areas for future work. For instance, the cost function may not accurately represent the real-world costs of production, and the marginal cost may not be constant over time. Future research could focus on developing more accurate cost functions and evaluating the marginal cost under different production levels and scenarios.

The following is a list of mathematical formulas and equations used in this article:

  • Cost Function: C(x)=5,000+50x−0.25x2C(x) = 5,000 + 50x - 0.25x^2
  • Derivative of Cost Function: C′(x)=50−0.5xC'(x) = 50 - 0.5x
  • Marginal Cost: C′(150)=−25C'(150) = -25
    Frequently Asked Questions (FAQs) on Marginal Cost

In our previous article, we explored the concept of marginal cost and evaluated it at a production level of 150 microwaves per month. However, we understand that there may be many questions and doubts that readers may have regarding marginal cost. In this article, we will address some of the frequently asked questions (FAQs) on marginal cost.

Q: What is marginal cost?

A: Marginal cost is the additional cost incurred by producing one more unit of a good or service. It is a measure of the rate of change of the total cost with respect to the quantity produced.

Q: Why is marginal cost important?

A: Marginal cost is an essential concept in economics and business as it helps in determining the optimal production level. It also helps in making informed decisions regarding pricing, production, and investment.

Q: How is marginal cost calculated?

A: Marginal cost is calculated by finding the derivative of the cost function with respect to the quantity produced. The derivative represents the rate of change of the total cost with respect to the quantity produced.

Q: What is the difference between marginal cost and average cost?

A: Marginal cost is the additional cost incurred by producing one more unit of a good or service, while average cost is the total cost divided by the quantity produced. Marginal cost is a measure of the rate of change of the total cost, while average cost is a measure of the total cost per unit.

Q: Can marginal cost be negative?

A: Yes, marginal cost can be negative. This occurs when the cost function is decreasing at a certain production level. In our previous article, we evaluated the marginal cost at a production level of 150 microwaves per month and found it to be -25.

Q: What are the implications of a negative marginal cost?

A: A negative marginal cost implies that the cost of producing one more unit of a good or service is decreasing. This can be beneficial for businesses as it allows them to produce more units at a lower cost.

Q: Can marginal cost be used to determine the optimal production level?

A: Yes, marginal cost can be used to determine the optimal production level. The optimal production level occurs when the marginal cost equals the marginal revenue. This is because at this level, the additional revenue generated by producing one more unit of a good or service equals the additional cost incurred.

Q: What are the limitations of marginal cost?

A: Marginal cost has several limitations. It assumes that the cost function is continuous and differentiable, which may not be the case in real-world scenarios. Additionally, marginal cost may not account for fixed costs, which can be significant in certain industries.

In conclusion, we have addressed some of the frequently asked questions (FAQs) on marginal cost. Marginal cost is an essential concept in economics and business that helps in determining the optimal production level and making informed decisions regarding pricing, production, and investment.

The following is a list of mathematical formulas and equations used in this article:

  • Cost Function: C(x)=5,000+50x−0.25x2C(x) = 5,000 + 50x - 0.25x^2
  • Derivative of Cost Function: C′(x)=50−0.5xC'(x) = 50 - 0.5x
  • Marginal Cost: C′(150)=−25C'(150) = -25