1. A competitive firm's production function is Q = 100 + 40L - .5L²+ 20K - .5*K², and its demand function is P_Q = MR_Q= d = $30. The prices of L and K are P_L = $4 and P_K = $12. Find the profit-maximizing amount of output Q.

1. A firm's objective is to Maximize Profits and Minimize Costs. Demand is Q = 600 - 3*P. The firm's production function is Q = 5*L^.6*K^.5. Total Cost is TC = P_L*L + P_K*K = $12*L + $6*K. The objective is to maximize Profit. Find the Profit-Maximizing output. At the profit-maximizing solution, K =