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