A representative firm with long-run total cost given by TC = 11.25 + 20q + 5q² operates in a competitive industry where the short-run market demandand supply curves are given by Q_D = 1,400 - 40P and Q_S = -400 + 20P. If it continues to operate in the long run, its profit maximizing level of output is?

I know the answer is 1.5, but am unsure of how to get to that answer. If I could be helped in showing how to get there, I would appreciate it.