Question

The total cost $C\left(x\right)$ 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 $17$ units are produced.

Answer 1

We know, marginal cost is the instantaneous rate of change of total cost at any level of output.
Let $M.C.$ be marginal cost, then

$M.C.=\frac{dC}{dx}$

Given, $C\left(x\right)=0.007x^3-0.003x^2+15x+4000$

$M.C.=\frac{d}{dx}\left[C\right(x\left)\right]$

$\Rightarrow M.C.$

$=\frac{d}{dx}[0.007x^3-0.003x^2+15x+4000]$

$\Rightarrow M.C.=0.007\left(3x^2\right)-0.003\left(2x\right)+15$

$\Rightarrow M.C.=0.021x^2-0.006x+15$

When $x=17$

$\Rightarrow M.C.=0.021\left({17}^2\right)-0.006\left(17\right)+15$

$\Rightarrow M.C=0.021\left(289\right)-0.102+15$

$\Rightarrow M.C=6.069-0.102+15$

$\Rightarrow M.C=20.967$

Hence, the Required Marginal cost is

$Rs20.967$