Three firms make up the sprockets industry and compete by choosing quantity to maximize profits. One firm is the leader (Firm 1), choosing its quantity first, and the remaining two firms (Firms 2 and 3) simultaneously choose quantity after the leader. The market inverse demand is given by p = 122.00 - 2Q, where pis the per-unit price, q is the output for Firm / (Firm 1, 2, or 3), and Q = q1 + q2 + 93. All firms face constant marginal costs of $2 per unit. Assume no fixed costs. What is the optimal output for Firm 1? (Round to two decimals if necessary.) What is the optimal output for Firm 2? (Round to two decimals if necessary.) What is the optimal output for Firm 3? (Round to two decimals if necessary.) Part 2 (0.7 point) See Hint What is the equilibrium price in this market? $ (Round to two decimals if necessary.)What is the prot for each rm? Firm 1 prot: $ (Round to two decimals if necessary.) Firm 2 prot: $ l (Round to two decimals if necessary.) Firm 3 prot: $ l (Round to two decimals if necessary.)