A firm's production process uses labor, $L$, and capital, $K$, and materials, $M$, to produce an output, $Q$ according to the function $Q = K L M$, where the marginal products of the three inputs are $M P _ { L }$ $= K M , M P _ { K } = L M$, and $M P _ { M } = K L$. The wage rate for labor is $w = 2$, the rental rate of capital is $r$ $= 1$, and the cost of materials is $m = 4$ per unit. Let materials input be fixed now at $M = 2$. What is the cost minimizing level of capital that the firm must use to produce a target level of output, $Q = 1600$ ?
A) $K = 5$
B) $K = 10$
C) $K = 20$
D) $K = 40$

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The Answer of A firm's production process uses labor, $L$, and capital, $K$, and materials, $M$, to produce an output, $Q$ according to the function $Q = K L M$, where the marginal products of the three inputs are $M P _ { L }$ $= K M , M P _ { K } = L M$, and $M P _ { M } = K L$. The wage rate for labor is $w = 2$, the rental rate of capital is $r$ $= 1$, and the cost of materials is $m = 4$ per unit. Let materials input be fixed now at $M = 2$. What is the cost minimizing level of capital that the firm must use to produce a target level of output, $Q = 1600$ ?
A) $K = 5$
B) $K = 10$
C) $K = 20$
D) $K = 40$

A Firm's Production Process Uses Labor LLL , and Capital KKK , and Materials

A Firm's Production Process Uses Labor $L$ , and Capital $K$ , and Materials