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 $M P _ { K } = 2 K L$ . 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) $( 90,30 )$