Profit maximizing

A dominant firm operates in various markets. In one of these markets, it is a monopolist and produces with the following cost function: C(q1) = 5q1. The market demand is P = 1005 - Q.

Find the profit maximizing P and q1 and profit. (I have worked out this part and got q1 = 500, P = 505 and profit = 249975).

A new fringe firm with C = 28,900 + (qf^2)/4 enters the market. The fringe firm acts as a rice taker and maximizes its profits. The dominant firm, after the entry , subtracts the fringe firm's supply and behaves as a monopolist for the residual demand. Find the new profit maximizing P, q1, qf and profits as well.