(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

You are a lab technician and must create 250 ml of a 17% solution. You have availible three stock solutions. You have a one liter container of a 5% salt, a 500 l contained of a 28% salt solution, and a 400 ml container of a 40% salt solution. Show the work necessary to calculate the cheapest ethod of preparing the 17% salt solution ifthe 5% solution costs $28 per liter, the 28% soltution costs $38 per liter, and the 40% solution costs $50 per liter.

So far I have this

2. Relavant equations

X+Y+Z=250

.05X+.28Y+.4Z=.17(250)

C(X,Y,Z)=(1/1000)(28X+38Y+50Z)

3. The attempt at a solution

I think I need a fourth equation so I can find the dervative and solve for 1 of the variables to optimize the solution,or I need to set derivative of the third equation = to 0, but I wouldn't know what to do from there.

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# Optimization with three variables

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