# The total cost C (x) in Rupees associated with the production of x units of an item is given by

Question:

The total cost (x) in Rupees associated with the production of x units of an item is given by

$C(x)=0.007 x^{3}-0.003 x^{2}+15 x+4000$

Find the marginal cost when 17 units are produced.

Solution:

Marginal cost is the rate of change of total cost with respect to output.

$\therefore$ Marginal cost $(M C)=\frac{d C}{d x}=0.007\left(3 x^{2}\right)-0.003(2 x)+15$

$=0.021 x^{2}-0.006 x+15$

When $x=17, \mathrm{MC}=0.021\left(17^{2}\right)-0.006(17)+15$

$=0.021(289)-0.006(17)+15$

$=6.069-0.102+15$

$=20.967$

Hence, when 17 units are produced, the marginal cost is Rs. 20.967.