A firm$$s profit function is:

$($q$)=$R$($q$)-$C$($q$)=140$q$-(325+40$q$+10$q$2)$

where the firm$$s revenue function is R$($q$)=140$q and the firm$$s cost function is $325+40$q$+10$q$2.$

What is $($a$)$ the output level that maximizes the firm$$s profit? At the profit maximizing level of output, what is

$($b$)$ the firm$$s revenue? What is $($c$)$ the firm$$s variable cost? What is $($d$)$ the firm$$s profit? And, finally, $($e$)$

should the firm operate or shut down in the short run?