The production function for a company is given by

f$($x$,$ y$)=100$x$0\mathrm{.}6$y$0\mathrm{.}4$

where x is the number of units of labor $($at $$48$ per unit$)$ and y is the number of units of capital $($at $$36$ per unit$).$ The total cost for labor and capital cannot exceed $$100,000.$

$($a$)$

Find the maximum production level for this manufacturer. $($Round your answer to the nearest integer.$)$

units

$($b$)$

Find the marginal productivity of money. $($Round your answer to three decimal places.$)$

$($c$)$

Use the marginal productivity of money to find the maximum number of units that can be produced when $$125,000$ is available for labor and capital.

units

$($d$)$

Use the marginal productivity of money to find the maximum number of units that can be produced when $$350,000$ is available for labor and capital.

units