A U$.$S$.$ synthetic rubber manufacturer is considering moving its production to a Japanese plant. Its production function is:

$q=L^{0\mathrm{.}50}{K}^{0\mathrm{.}50}(basedon$ Flath, $2011).$

In the United States, $w=$$$10=r.$ At its Japanese plant, the firm will pay a $40\%$ lower wage and a $40\%$ higher cost of capital: $w^{***}=$$$7\mathrm{.}14$ and $r^{***}=14\mathrm{.}00.$ What are $L$ and $K$ and what is the cost of producing $q=100$ units in both countries? $($for all responses, enter a real number rounded to two decimal places$)$ In the U$.$S$.,L$ is