Podcast
Questions and Answers
What is the formula for marginal cost (MC) derived from the total cost function $C(x) = 0.0013x^3 + 0.002x^2 + 5x + 2200$?
What is the formula for marginal cost (MC) derived from the total cost function $C(x) = 0.0013x^3 + 0.002x^2 + 5x + 2200$?
- MC = 0.0013x^2 + 0.004x + 5
- MC = 0.00039x^2 + 0.004x + 5 (correct)
- MC = 0.00013x^2 + 0.002x + 5
- MC = 0.00039x^2 + 0.002x + 5
What is the first step in calculating the marginal cost when 150 items are produced?
What is the first step in calculating the marginal cost when 150 items are produced?
- Substituting $x = 150$ into the cost function $C(x)$
- Finding the average cost for producing 150 items
- Calculating the total cost for producing 150 items
- Taking the first derivative of the cost function $C(x)$ (correct)
After calculating, what is the marginal cost when producing 150 items?
After calculating, what is the marginal cost when producing 150 items?
- 13.975 rupees
- 14.375 rupees (correct)
- 15.000 rupees
- 14.575 rupees
What does the term 'marginal cost' represent in the context of production?
What does the term 'marginal cost' represent in the context of production?
Which of the following statements about the marginal cost function is correct?
Which of the following statements about the marginal cost function is correct?
Flashcards
Marginal Cost
Marginal Cost
The approximate cost of producing one additional item.
Total Cost Function
Total Cost Function
Represents the total cost of producing a given number of items.
Derivative of a function
Derivative of a function
The rate of change of a function with respect to its variable.
Finding Marginal Cost
Finding Marginal Cost
Signup and view all the flashcards
Application of Derivatives (Marginal Cost)
Application of Derivatives (Marginal Cost)
Signup and view all the flashcards
Study Notes
Cost Function and Marginal Cost
- The cost function for producing 𝑥 items in a factory each day is given by 𝐶(𝑥) = 0.00013𝑥³ + 0.002𝑥² + 5𝑥 + 2200.
- Marginal cost (MC) is the derivative of the total cost function with respect to the quantity produced (𝑥).
- To find the marginal cost, differentiate the cost function: MC = d𝐶(𝑥)/d𝑥.
- MC = 0.00039𝑥² + 0.004𝑥 + 5.
- The marginal cost when 150 items are produced is found by substituting 𝑥 = 150 into the marginal cost equation.
- MC(150) = 0.00039(150)² + 0.004(150) + 5 = 8.775 + 0.6 + 5 = 14.375.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your understanding of cost functions and marginal cost calculations. This quiz will challenge you to differentiate cost functions and evaluate marginal cost at a given production level using the provided formulas.
