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 that the firm wants to produce 27,000 units of output in the most efficient way possible. How much does the firm spend?

A) $600
B) $900
C) $1,500
D) $2,100