math
posted by Fatih on .
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.

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. 
??I got this when I followed steve's steps...
optimal solution: c=191/23; x=2750/23; y=3000/23; z=0 
my x and y are in ml not liters..