Suppose a Cobb$-$Douglas Production function is given by the following:

$P(L,K)=90L^{0\mathrm{.}9}{K}^{0\mathrm{.}1}$

where $L$ is units of labor, $K$ is units of capital, and $P(L,K)$ is total units that can be produced with this

labor$/$capital combination. Suppose each unit of labor costs $$200$ and each unit of capital costs $$1,600.$

Further suppose a total of $$480,000$ is available to be invested in labor and capital $($combined$).$

A$)$ How many units of labor and capital should be "purchased" to maximize production subject to your

budgetary constraint?

Units of labor, $L=$

Units of capital, $K=$

B$)$ What is the maximum number of units of production under the given budgetary conditions? $($Round your

answer to the nearest whole unit.$)$

Max production $=$

units