The world is suffering from a new virus outbreak. In July, firm 1 successfully developed the first vaccine and sold q1 amount of vaccines to the world. Seeing firm 1's success, firm 2 decided to develop its own vaccine as well. In September, firm 2 successfully developed and sold q2 amount of its vaccine. Vaccine development requires a substantial initial investment of f = 10000, but the marginal cost of vaccine production is relatively low at c = 10 for both firms. The world's demand for the vaccine is Q = 500 p. Assume the vaccines developed by firms 1 and 2 are perfectly substitutable (i.e., equal efficacy, risk, etc.). 1. How many vaccines would firm 2 produce to maximize profit? Note that the optimal q2 will depend on q1, since firm 2 observes q1 before deciding q2