A company has fixed costs of $$4,500.$ Producing $450$ items incurrs a total cost of $$15,750.$

$($a$)$ Find the total cost function, $C(x)=$

$($b$)$ What is this company's marginal cost?

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

$($c$)$ What is the company's average cost of producing $401$ items?

$\frac{?}{\text{b}\text{a}\text{r}}(C)(401)=$$$,$ litem

$($round to two decimal places$)$