You are a lab technician and must create 250 ml of a 17% salt solution. You have

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.

Explanation / Answer

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

then from the data

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:
cost = 8.30435 $
x = 0.119565 L
y = 0.130435 L
z = 0 L

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