Suppose that a firm's production function is given by Y = 12 K L - L2, where K is the level of capital and L is the number of laborers the firm employs. For the given production function the marginal products are, MPL = 12 K - 2 L and MPK = 12 L. The rental rate of capital is $45 while the wage rate is $15. What is the cost minimizing level of capital (K*) if the firm is producing 500 units of output?
