Question

Let the production function of a firm be:
$Q=5L^{1/2}{K}^{1/2}$

Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.

Answer 1

Given,
$Q=5L^{1/2}{K}^{1/2}$
$Q=5\left(100{)}^{1/2}\right(100{)}^{1/2}$
$=5\left({10}^2{)}^{1/2}\right({10}^2{)}^{1/2}$
$=5\times 10\times 10=500$
The maximum output the firm can produce with 100 units of L and 100 units of K is 500.