Question $2($Cournot competition$).$ Assume demand is $100-$ p$.$ Two firms have constant but different marginal costs: cost function for firm $A$ is $10q$ and cost function for firm $B$ is $15q.$ Suppose in equilibrium the two firms produce $q_A$ and $q_B$ respectively. What are $q_A$ and $q_B?$ What is the profit for each firm?

Question $3($Collusion$).$ Consider the setting in Question $2.$ Suppose the two firms collude to maximize the sum of the two firms' profits. What will be the total profit of the two firms?