You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w (price of labor) = $40, r (price of capital) = $100, MP_L = 20, and MP_K = 40 is the firm minimizing cost?

(b)The production function for a competitive firm is Q = K^0.5L^0.5. The firm sells its output at a price of $10 and can hire labor at a wage of $5.

Marginal Product of labor =

Capital is fixed at 25 units. What is the profit-maximizing quantity of labor?