A Firm's Production Function Is Given By $Q = K ^ { 2 } L$

Multiple Choice

A firm's production function is given by $Q = K ^ { 2 } L$ . The marginal products of labor and capital are, respectively, $$M P _ { L } = K ^ { 2 }$$ and $$M P _ { X } = 2 K L$$ . Further, the wage rate is $w = \$ 10$ and the rental rate of capital is $r = \$ 20$ . Suppose the firm wants to produce 27,000 units of output. What is the most efficient combination of labor and capital $( L , K )$ ?

A) (20, 20)
B) (30, 30)
C) (30, 90)
D) (90, 30)