HarMathAp$1211,1\mathrm{.}043.$

Suppose that the total cost $($in dollars$)$ for a product is given by

$C(x)=1300200ln(2x1)$

where $x$ is the number of units produced.

$($a$)$ Find the marginal cost $\frac{?}{\text{b}\text{a}\text{r}}(MC)$ function.

$\frac{?}{\text{b}\text{a}\text{r}}(MC)=$

$$

$($b$)$ Find the marginal cost when $200$ units are produced. $($Round your answer to the nearest cent.$)$

$

Interpret your result.

The profit from the next unit will be approximately this amount.

This is the total profit from producing $200$ units.

It will cost approximately this amount to make the next unit.

This is the total cost of producing $200$ units.

$($c$)$ Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function?

$\frac{?}{\text{b}\text{a}\text{r}}(MC)0$

$\frac{?}{\text{b}\text{a}\text{r}}(MC)<mn>0</mn>$

ANC$>0$

$MC0$

$MC=0$

Does it apply in this problem?

Yes

No