A firm's production function is: Q = K1/2 L1/2. Suppose that capital is fixed at 81 units. If the firm can sell its output at a price of $100 per unit, hire labor at $50 a unit, and rent capital at $10 a unit, how many units of labor should the firm hire to maximize profits? Given your answer, what is the level of output that maximizes profits. Lastly, calculate the level of profits at the profit-maximizing level of labor and output given that capital is fixed at 81 units.