Question:
The Total Variable Cost (TVC) for a firm is given by TVC = $x^3-bx^2$. The Total Fixed Cost is 848. The value of b for which the Marginal Cost is minimum at x = 16 is________ (in integer).
The Total Variable Cost (TVC) for a firm is given by TVC = $x^3-bx^2$. The Total Fixed Cost is 848. The value of b for which the Marginal Cost is minimum at x = 16 is________ (in integer).
Updated On: Nov 26, 2025
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Correct Answer: 48
Solution and Explanation
Given the Total Variable Cost (TVC) function: TVC = x3 - bx2. We need to find the value of b that minimizes the Marginal Cost (MC) at x = 16.
Step 1: Derive the Marginal Cost Function
Marginal Cost (MC) is the derivative of TVC with respect to x:
MC = d(TVC)/dx = 3x2 - 2bx
Step 2: Find the Condition for Minimum MC
To minimize the MC at x = 16, set the derivative of MC with respect to x to zero:
MC' = d(MC)/dx = 6x - 2b
Setting MC' to zero at x = 16:
MC'(16) = 6(16) - 2b = 0
96 - 2b = 0
Step 3: Solve for b
Rearranging the equation gives:
2b = 96
b = 48
Conclusion: The value of b that minimizes Marginal Cost at x = 16 is 48.
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