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Posted by on Wednesday, February 15, 2012 at 8:44am.

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.

  • math - , Wednesday, February 15, 2012 at 1:56pm

    let c = cost of final solution
    use x,y,z liters of the three solutions

    x <= 1.0
    y <= .5
    z <= .4

    x + y + z = .25
    .05x + .28y + .40z = .17*.25

    c = 28x + 38y + 50z

    A little manipulation of tableaux (a google on linear programming will turn up zweigmedia) will show that

    Optimal Solution: c = 8.89; x = 0.164, y = 0, z = 0.086

    Hmmm. no 28% solution used.

  • math - , Thursday, April 12, 2012 at 4:50pm

    ??I got this when I followed steve's steps...
    optimal solution: c=191/23; x=2750/23; y=3000/23; z=0

  • math - , Thursday, April 12, 2012 at 4:54pm

    my x and y are in ml not liters..

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