Suppose a company has fixed costs of $$39,200$ and variable cost per unit of $\frac{2}{5}x+444$ dollars, where $x$ is the total number of units produced. Suppose further that the selling price of its product is $1872-\frac{3}{5}x$ dollars per unit.

$($a$)$ Find the simplified cost function $.$

$C(x)=$

$$

$($b$)$ Find the simplified revenue function $R(x).$

$R(x)=$

$$

$($c$)$ Form the profit function $P(x).$

$P(x)=$

$$