I have completed this problem, but I am not sure if I did it right.

For part 1.1, I got q1(q2) = 99/2 - q2/2 and q2(q1) = 99/2 - q1/2

For part 1.2, I got q1 = 33 and q2 = 33.

Please verify I have the correct solution and include steps to make sure I did it right.

Consider a market with two firms. Demand in this market is given by p(Q) = 100Q. The two firms have identical cost functions equal to C(q) = 10q. Suppose the two firms are engaged in Cournot competition, meaning that they each set their quantity independently andQ=q1+q2.

1.1. What is each firm's best response function?

1.2. What is each firm's Nash equilibrium quantity and profit?