Ex$.1$ The demand function for C$.$O$.$B$.$ T$-$shirts is given by

$q=-40p+600$

where $q$ is the number of $T-$shirts that can be sold in one week at the price of $$p$ per shirt. The fixed costs are $$400$ per week, and the T$-$shirts cost $$5$ each.

$($a$)$ Find the weekly profit as a function of $p.$

$($b$)$ Determine the unit price that should be charged to obtain the largest weekly profit.

$($c$)$ What is the largest weekly profit?