A Firm's Production Function Is Given By $Q = K L$

Multiple Choice

A firm's production function is given by $Q = K L$ . The marginal products of labor and capital are, respectively, $M P _ { L } = K$ and $M P _ { K } = L$ . The wage rate of labor 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 yields a cost of exactly $\$ 1000$ ?

A) $( 10,45 )$
B) $( 25,50 )$
C) $( 50,25 )$
D) $( 20,40 )$