The total cost C(x) in Rupees, associated with the production of x units of an item is given by $C (x) = 0 .005 x^{3} - 0 .02 x^{2} + 30 x + 5000$ .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.

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30.02

30.05

answer is C.

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Detailed Solution

Since marginal cost is the rate of change of total cost with respect to the
output, we have Marginal cost $= \frac{dC}{dx} = 0 .005 (3 x^{2}) - 0 .02 (2 x) + 30$
When ,
$\begin{aligned} x = 3, MC = 0 .015 (3^{2}) - 0 .04 (3) + 30 \\ = 0 .135 - 0 .12 + 30 = 30 .015 \end{aligned}$
Hence, the required marginal cost is Rs. 30.02 (nearly).