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 that the firm spends exactly $\$ 1200$ in the most efficient way possible. How much output can the firm produce?

A) 50,000
B) $56,406.25$
C) 60,750
D) 64,000