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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 $C(x) = 0.0013x^3 + 0.002x^2 + 5x + 2200$?
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?
After calculating, what is the marginal cost when producing 150 items?
After calculating, what is the marginal cost when producing 150 items?
What does the term 'marginal cost' represent in the context of production?
What does the term 'marginal cost' represent in the context of production?
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Which of the following statements about the marginal cost function is correct?
Which of the following statements about the marginal cost function is correct?
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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.
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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.
