Assume that a local train station has a monopoly over train rides. The firm has estimated that its market demand curve can be drawn from the following equation P $=60(1/2)$ Q$.$ Let MC $=$ AC $=15.$ The firm has determined that younger consumers $($under $50)$ are willing to pay up to $$30$ per ticket for a train ride and that older consumers $(50$ or older$)$ are willing to pay up to $$50$ per ticket for a train ride. If the firm price discriminates what is their profit?