Suppose you are the manager of a firm that operates in a monopolistically competitive industry. The market demand function facing your firm is QD $=3605$P and your firm$$s cost function is C$($Q$)=2+50$Q $+2$Q$2.$

$($a$)$ Find the inverse demand function for your firm$$s product.

$($b$)$ Determine the profit$-$maximizing price and level of production.

$($c$)$ Calculate your firm$$s maximum profits.

$($d$)$ What long$-$run adjustments should your firm expect? Explain.