The total cost C (x) associated with the production of x units of an item is given by
Question:

The total cost $C(x)$ 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:

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

Marginal Cost (MC) $=\frac{d C}{d x}(x)=\frac{d}{d x}\left(0.007 x^{3}-0.003 x^{2}+15 x+4000\right)=0.021 x^{2}-0.006 x+15$

When $x=17$

Marginal Cost $(M C)==0.021(17)^{2}-0.006(17)+15=6.069-0.102+15=R s 20.967$

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