Question

The total cost C(x) in rupees associated with the production of x units of an item is given by $C\left(x\right)=0.007x^3-0.003x^2+15x+4000$.

Find the marginal cost when x=17 units are produced.

Answer 1

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

$\therefore$ Marginal Cost $\left(MC\right)=\frac{dC}{dx}=0.007\left(3x^2\right)-0.003\left(2x\right)+15=0.021x^2-0.006x+15$
when x= 17, $MC=0021(17{)}^2-0.006(17)+15=0.021(289)-0.006(17)+15=6.069-0.102+15=20.967$
Hence, when 17 units are produced. the marginal cost is Rs. 20.967.