Question

A doll making small-scale unit calculates the variable cost of making x number of dolls per day as three times the square of \(x\). The fixed cost of packaging x dolls is  \(₹ 2800\). The marginal cost of producing 120 dolls:

• A. \(₹ 72\)
• B. \(₹ 720\)
• C. \(₹ 2872\)
• D. \(₹ 3520\)

Answer 1

The Correct Option is B

The variable cost, \( VC(x) \), of producing \( x \) dolls is given by \( VC(x) = 3x^2 \). The fixed cost for packaging \( x \) dolls is \( ₹2800 \). Therefore, the total cost \( TC(x) \) is:

\( TC(x) = VC(x) + \text{Fixed Cost} = 3x^2 + 2800 \)

The marginal cost is the derivative of the total cost with respect to \( x \), denoted by \( MC(x) \). Thus, find the derivative \( TC'(x) \):

\( \frac{d}{dx}(3x^2 + 2800) = 6x \)

To find the marginal cost of producing 120 dolls, substitute \( x = 120 \) into the derivative:

\( MC(120) = 6 \times 120 = 720 \)

Thus, the marginal cost of producing 120 dolls is \( ₹720 \).