SOLUTION: A chemist has four solutions of a very rare and expensive chemical that at 15% acid (cost $120 per ounce), 20% acid (cost $180 per ounce), 35% acid (cost $280 per ounce) and 45% ac
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Question 511614: A chemist has four solutions of a very rare and expensive chemical that at 15% acid (cost $120 per ounce), 20% acid (cost $180 per ounce), 35% acid (cost $280 per ounce) and 45% acid (cost $359 per ounce). She requires 200oz of a 29% solution. Find the combination of any two of these concentrations that will minimize the total cost of the mix.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A chemist has four solutions of a very rare and expensive chemical that at 15% acid (cost $120 per ounce), 20% acid (cost $180 per ounce), 35% acid (cost $280 per ounce) and 45% acid (cost $359 per ounce). She requires 200oz of a 29% solution. Find the combination of any two of these concentrations that will minimize the total cost of the mix.
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120/15 = $8 per %
180/20 = $9
280/35 = $8
359/45 = $7.9777.. the least expensive.
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The average of 15% and 45% is 30%, close to 29% and the 2 least expensive.
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f = amount of 45%
t = amount of 15%
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f + t = 200 (total mixture)
0.45f + 0.15t = 0.29*200
t = 200 - f
45f + 15t = 5800
45f + 15*(200-f) = 5800
45f + 3000 - 15f = 5800
30f = 2800
f = 93.333 of 45%
t = 106.667 of 15%
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I think it's the best fit, I'll check it tomorrow.
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Would have been a more interesting problem if any of the 4 could be used.
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