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 $r = \$ 20$ . What is the most efficient combination of labor and capital $( L , K )$ that also results in a total cost level of exactly $\$ 1,200$ ?

A) $( 20,50 )$
B) $( 25,47.5 )$
C) $( 30,45 )$
D) $( 40,40 )$