CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
The total cost function of a Pune-based firm is C(x) = 2x² + 30x + 500 (in rupees), where x is the number of units produced. What is the marginal cost when x = 20?
The marginal cost is ₹110. Marginal cost is the first derivative of the total cost function, which is 4x + 30, and substituting x = 20 gives 4 times 20 plus 30, equal to 110 rupees per additional unit.
- A₹80
- B₹110Correct
- C₹70
- D₹1,900
Explanation
Marginal cost is the derivative of total cost: MC = 4x + 30. At x = 20, MC = 80 + 30 = 110. The value 80 results from ignoring the constant 30 in the derivative, and 1,900 is the total cost, not the marginal cost.
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