Suppose the production function for a product is

Q $=85$K$3/5$L$2/5$

where K is the capital expenditures and L is the number of work$-$hours.

$($a$)$

Find the marginal productivity of K $($MPK$).$

$($b$)$

Find the marginal productivity of L $($MPL$).$

$($c$)$ Evaluate the marginal productivity ofK$($MPK$)$ when the firm uses$50$units of labor $($L$)$ and$100$units of capital $($K$).($round to the next unit$)$

MPK $=$

Explain the economic meaning of your answer above:

$($d$)$ Evaluate the marginal productivity ofL$($MPL$)$ when the firm uses$50$units of labor $($L$)$ and$100$units of capital $($K$).($round to the next unit$)$

MPL $=$

Explain the economic meaning of your answer above:

$($e$)$ Now suppose that this company's cost constraint is the following:

$200$K $+150$L $=27500$

$.$

Given the cost constraints, what values of K and L will maximize production? $($round to the next unit$)$

K $=$ units

L $=$ units

What is the highest level of production possible given the cost constraint? $($round to the next unit$)$

Q $=$ units