Suppose a Cobb$-$Douglas Production function is given by

$P(L,K)=10L^{00\mathrm{.}75}{K}^{0\mathrm{.}25}$

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 $$700$ and each unit of capital costs $$2,100.$ Further suppose a total of $$504,000$ 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 the budgetary constraint? Round to the nearest whole number, if necessary.

Labor: $L=$ units

Capital: $K=$ units

b$.$ What is the maximum number of units of production under the given budgetary conditions? Round to the nearest whole number, if necessary.

Maximum production: units