The total cost $C(x)$ in Rupees, associated with the production of $x$ units of an item is given by $C(x) = 0.005 x^3 - 0.02 x^2 + 30x + 5000$. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

₹30.015

The correct answer is Option (3) → ₹30.015 ##

Since marginal cost is the rate of change of total cost with respect to the output, we have

$\text{Marginal cost (MC)} = \frac{dC}{dx} = 0.005(3x^2) - 0.02(2x) + 30$

When $x = 3$,

$\text{MC} = 0.015(3^2) - 0.04(3) + 30$

$= 0.135 - 0.12 + 30 = 30.015$

Hence, the required marginal cost is ₹30.015.