please help me solve this.

2. Consider the following variant of the Cournot Model: There are two firms producing a homogenous good with (inverse) demand given by P = 2000 - 10Q. Each firm has a constant marginal cost c = 200 and the two firms compete by choosing their output simultaneously. a. Find the Cournot-Nash Equilibrium of this game. What are the firms' profits in equilibrium (10 pts) b. Suppose that the two firms were to merge and become a monopoly. How much output will the monopoly produce? What are the monopoly's profits(5 pts) c. Suppose that instead of merging the two firms agree to produce half of the monopoly output with each firm earning half of the monopoly profit. Is this a Nash Equilibrium? Explain why or why not. (5 pts)