Posted by Fatih 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  Steve, 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  James, 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  James, Thursday, April 12, 2012 at 4:54pm
my x and y are in ml not liters..