A chemical manufacturing plant can produce $z$ units of chemical $Z$ given $p$ units of chemical $P$ and $r$ units

of chemical R$,$ where:

$z=40p^{\mathrm{.}5}{r}^{0\mathrm{.}5}$

Chemical $P$ costs $$300$ a unit and chemical $R$ costs $$900$ a unit. The company wants to produce as many

units of chemical $Z$ as possible with a total budget of $$72,000.$

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 $P,p=$

Units of chemical $R,r=$

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, $z=$ Solve it in python.