Question:
The total cost C (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.