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).

Answer 1

Correct Answer: 48

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.