(Solved): A chemical manufacturing plant can produce \( z \) units of chemical Z given \( p \) units of chem ...

A chemical manufacturing plant can produce \( z \) units of chemical Z given \( p \) units of chemical \( \mathrm{P} \) and \( r \) units of chemical R, where: \[ z=80 p^{0.84} r^{0.16} \] Chemical \( P \) costs \( \$ 500 \) a unit and chemical \( R \) costs \( \$ 3,500 \) a unit. The company wants to produce as many units of chemical \( \mathrm{Z} \) as possible with a total budget of \( \$ 656,250 \). A) How many units each chemical ( \( \mathrm{P} \) and \( \mathrm{R}) \) 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, \( z= \) units