Question

The total cost $C (x)$ in Rupees associated with the production of $x$ units of an item is given by $c(x)=0.007x^3-0.003x^2+15x+4000$.
Find the marginal cost when 17 units are produced.

Answer 1

The correct answer is Rs. 20.967.
Marginal cost is the rate of change of total cost with respect to output.
∴ Marginal cost (MC)$=\frac{dc}{dx}=0.007(3x^2)-0.003(2x)+15$
$=0.021x^2-0.006x+15$
When $x = 17, MC = 0.021 (17^2 ) − 0.006 (17) + 15$
$= 0.021(289) − 0.006(17) + 15$
$= 6.069 − 0.102 + 15$
$= 20.967$
Hence, when 17 units are produced, the marginal cost is Rs. 20.967.