A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where:(adsbygoogle = window.adsbygoogle || []).push({});

z=90 p^.5 r^0.5

Chemical P costs $400 a unit and chemical R costs $3,200 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $320,000.

First thing I did was find the constraint being 400p+3200r=320,000, then solved for p=800-8r

plugged that into the first eqn z=90(800-8r)^.5*r^.5

Then I got z=1800(2r)^.5-720r, took the derivative z'=(1800/(2r^.5))-720 set it equal to zero and solved for r. I got r=25/4

then plugged that into the eqn to solve for p, 400p+3200(25/4)=320,000, p=758.

Plugged both of those into the original eqn to find z=90(758)^.5*(25/4)^.5=6194.65...

Somewhere I'm wrong, not quite sure any guidance would help. Thanks

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# Homework Help: Optimizating problem

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