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 the firm wants to produce 27,000 units of output. What is the most efficient combination of labor and capital $( L , K )$ ?
A) $( 20,20 )$
B) $( 30,30 )$
C) $( 30,90 )$
D) $( 90,30 )$

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The Answer of 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 the firm wants to produce 27,000 units of output. What is the most efficient combination of labor and capital $( L , K )$ ?
A) $( 20,20 )$
B) $( 30,30 )$
C) $( 30,90 )$
D) $( 90,30 )$

A Firm's Production Function Is Given By Q=K2LQ = K ^ { 2 } LQ=K2L

A Firm's Production Function Is Given By $Q = K ^ { 2 } L$