Achemical manufacturing plant can produce units of chemical z given units of chemical p and units of chemical r, where:

z=190*p0.84*r0.16

chemical p costs $200 a unit and chemical r costs $400 a unit. the company wants to produce as many units of chemical z as possible with a total budget of $150,000.

a) how many units each chemical (p and r) should be "purchased" to maximize production of chemical z subject to the budgetary constraint?
b) what is the maximum number of units of chemical z under the given budgetary conditions?