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

Total cost C(x) in Rupees associated with the production of x units of an item is given by,
$\bf{C(x)=0.007x^3-0.003x^2+15x+4000}$

if you know , Marginal cost (MC) is the rate of change of total cost with respect to output.
so, differentiate C(x) with respect to x,
$\bf{\frac{dC(x)}{dx}=0.021x^2-0.006x+15}$
so, when x = 17,
marginal cost = dC(x)/dx = 0.021(17)² - 0.006(17) + 15 =  0.021(289) – 0.102 + 15
= 20.967 Rs.

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