A chemical manufacturing plant can produce $\displaystyle {z}$ units of chemical Z given $\displaystyle {p}$ units of chemical P and $\displaystyle {r}$ units of chemical R, where:

$\displaystyle {z}={110}{p}^{{.5}}{r}^{{0.5}}$

Chemical P costs $500 a unit and chemical R costs $2,500 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $250,000.

A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint?

Units of chemical P, $\displaystyle {p}$ =

Units of chemical R, $\displaystyle {r}$ =

B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.)

Max production, $\displaystyle {z}$= units