Please help me find the answer to part 7 and part 8 with an explanation Thank you

In 2056, there are two mining firms operating on the moon, extracting Helium 3. Once both firms have entered the market, they compete a la Cournot. The market inverse demand function is given by P(Q) = 8 - Q. For the following items, we will modify the game. Firm 2 now has a Research & Devel- opment department capable of reducing marginal costs-but at a cost. Total research and installation costs, given a choice of c2 E [0, 3], are f(c2) = 6 -2c2. So, given a choice of c2, total costs are C2(q) = f(c2) + c2q = 6 - 2c2 + c2q. That is, firm 2 can set up a plant with marginal cost c2 = 3 paying no fixed cost. Alternatively, if it wants to set up a plant with marginal cost 1, the fixed cost would be 4. Firm 1 still has the same technology, with total cost C1(q) = 2 + 2q. The game has three stages. In the first, firm 1 enters and chooses the quantity q1. In stage 2, firm two enters, deciding its marginal cost c2. At the last stage, firm 2 chooses its quantity produced and "the market" determines the price given the quantities produced by both firms. The "big picture" question is, what is the subgame perfect Nash equilibrium of this game? We will proceed step by step. 7. What is the equilibrium quantity chosen by firm 1? 8. What are the equilibrium price, quantities, and profits in the market