Suppose That a Firm's Production Function of Output $Q$ Is a Function of Only Two Inputs, Labor (L) and a Function

Multiple Choice

Suppose that a firm's production function of output $Q$ is a function of only two inputs, labor (L) and capital $( K )$ and can be written $Q = 25 L K$ with marginal products $M P _ { L } = 25 K$ and $M P _ { K } =$ $25 L$ . Letting the wage rate for labor be $w$ and the rental rate of capital be $r$ , the equation for the firm's demand for labor would be:

A) $L = \sqrt { \frac { w Q } { 25 r } }$
B) $L = \sqrt { \frac { 25 r } { w Q } }$
C) $L = \sqrt { \frac { r Q } { 25 w } }$
D) $L = \sqrt { \frac { 25 w } { r Q } }$