You are a lab technician and must create 250 ml of a 17% salt solution. You have
ID: 3341995 • Letter: Y
Question
You are a lab technician and must create 250 ml of a 17% salt solution. You have available three stock solutions. You have a one liter container of a 5% salt, a 500 ml container of a 28% salt solution, and a 400 ml container of a 40% salt solution. Show the work necessary to calculate the cheapest method of preparing the 17% salt solution if the 5% salt solution costs $28 per liter, the 28% solution costs $38 per liter, and the 40% solution costs $50 per liter. Be sure to explain in paragraph form why you have selected the amounts of each and the total cost of your selection. I understand you can set it up using linear programming, but alas I don't know how to solve linear programming problems so if someone could show me a different way or walk through the steps that would be awesome!
Explanation / Answer
One way to do it is to convert concentrations in % to g/L to Molar concentrations. Then you can use M1Vi = M2V2 and solve for V2.
Hint:
The costs are linear, so you can either prepare it with 5%+28% or 5%+40%.
Calculate the cost of each and use the less expensive option.
I have the impression that it costs less by mixing 5% with 40%.
X+Y+Z=250
.05X+.28Y+.4Z=.17(250)
C(X,Y,Z)=(1/1000)(28X+38Y+50Z)
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