# math

posted by .

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 -

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 -

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

• math -

my x and y are in ml not liters..