The total cost N(x) in rupees, associated with the production of x units of an item is given by N(x)=0.06x3-0.01x2+10x-43. Find the marginal cost when 5 units are produced

The correct option/answer is Rs. 14.4.

Step-by-step Explanation:

Marginal cost represents the rate of change of the total cost with respect to the output (number of units produced). In mathematical terms, if $N\left(x\right)$ is the total cost function for producing $x$ units, then the marginal cost $MC$ is the first derivative of the total cost function with respect to $x$:

$MC=\frac{d}{dx}\left[N\left(x\right)\right]$

Given the total cost function:
$N\left(x\right)=0.06x^3-0.01x^2+10x-43$

We differentiate $N\left(x\right)$ with respect to $x$ term by term using the power rule of differentiation, which states that $\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$:

$MC=\frac{d}{dx}\left(0.06x^3-0.01x^2+10x-43\right)$

$MC=0.06·\left(3x^2\right)-0.01·\left(2x\right)+10·\left(1\right)-0$

$MC=0.18x^2-0.02x+10$

Now, we need to find the marginal cost when $x=5$ units are produced. Substituting $x=5$ into the marginal cost equation:

$MC=0.18{\left(5\right)}^2-0.02\left(5\right)+10$

$MC=0.18·\left(25\right)-0.1+10$

$MC=4.5-0.1+10$

$MC=4.4+10$

$MC=14.4$

Thus, the marginal cost when 5 units are produced is Rs. 14.4.