Please help me solve part 5 part 6 and part 7 with an explanation of how to find the answerThank you

In 2056, there are two mining rms operating on the moon, extracting Helium 3. Once both rms 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 85 Devel- opment department capable of reducing marginal costsbut at a cost. Total research and installation costs, given a choice of 02 E [0, 3], are f(02) = 6 262. So, given a choice of C2, total costs are 020;) = f(62) + egg = 6 202 + czq. That is, rm 2 can set up a plant with marginal cost C2 = 3 paying no xed 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 Cl (q) = 2 + 2:}. The game has three stages. In the rst, rm 1 enters and chooses the quantity in. In stage 2, rm two enters, deciding its marginal cost :22. At the last stage, firm 2 chooses its quantity produced and \"the market\" determines the price given the quantities produced by both rms. The \"big picture\" question is, what is the subgame perfect Nash equilibrium of this game? We will proceed step by step. 5. What is the protmaximizing marginal cost choice c2031)? 6. Given your last answer, what does rm 1 expect the quantity chosen by rm 2 to be, given its own choice of quantity? That is, what is the q2(q1) anticipated in the rst stage? 7. What is the equilibrium quantity chosen by rm 1