Please see the question below:

3. Consider a market with two firms, where demand is given by P = 400 - (q1 + 92) Firm 1 is the incumbent who moves first by buying up some capacity, which is the only input of production. Firm 2 is a potential entrant, who observes the incumbent's capacity choice and then decides to enter or not. If entry occurs, the firms compete by setting quantities simultaneously. Every unit of output requires one unit of capacity as input; capacity costs $40 per unit. The incumbent has no fixed costs. The entrant's fixed costs are $10,000. a. Suppose the incumbent purchases Kj units of capacity. Derive R1 (q2; K, ), its best response function in the post-entry game. b. Derive R2(q1), the entrant's best response function in the post-entry game. c. What quantities are produced at the worst post-entry Nash Equilibrium for the entrant? Show your work. d. Compute the limit quantity qf. Show your work. e. Based on your answer in (c) and (d), can you say whether the entrant will enter the market or not? Explain