A plant's production function is Q = 2KL + K . For this production function, MPK = 2L + 1 and MPL = 2K. The price of labor services w is $4 and of capital services r is $5 per unit.
a) In the short run, the plant's capital is fixed at K = 9. Find the amount of labor it must employ to produce Q = 45 units of output.
b) How much money is the firm sacrificing by not having the ability to choose its level of capital optimally?