A commodity has a demand function modeled by $p=108-0\mathrm{.}5x$ and a total cost function modeled by $C=30x+31\mathrm{.}75,$ where $x$ is the number of units.

$($a$)$ What price yields a maximum profit?

$

per unit

$($b$)$ When the profit is maximized, what is the average cost per unit? $($Round your answer to two decimal places.$)$

$ per unit