I may be over-complicating things, but something doesn't seem right (and I swear this isn't homework, I'm friggin 30 years old :P).
I want to see what it will cost me to make a TWO liter of Coca-Cola using coke syrup and CO2 (assume the water is free). Assume CO2 costs 0.21usd per liter of water (25usd for 120 liters).
The coke syrup needs to be diluted at a "5.4:1" ratio with the carbonated water. So how much will it cost me to make my own 2-liter?
Here's what I've done so far:
syrup cost per liter = C / ((G * D) * 3.785)
where
- C is the cost of G gallons of coke syrup
- D is the dilution (5.4), and
- 3.785 converts gallons to liters
For a 65.00usd box of 5 gallons of coke syrup, I get a cost of 0.64usd per liter. Along with CO2 cost, that makes it 1.69usd for a 2-liter.
That seems very, very costly, given that 2-liters in the store usually cost much less. If I'm wrong, where am I going wrong? If I'm right, why don't restaurants use 2-liters instead of fountain machines to increase their profits/lower their costs? I know they charge a lot for a glass of coke (and refills), not a 2-liter, but it still seems like it would make them more money.
I put that equation into an Excel sheet, and it seems like the syrup would have to be 30usd in order to get the cost down to 1.00usd/2-liter, and that doesn't even seem like much of a gain over buying 2-liter bottles from a grocery (especially with the equipment overhead costs). I spoke to a restaurant manager, and his cost is 56usd for a 5-gallon box, which puts the per 2-liter cost at $1.51 by my calculations, so that's when I suspected I was doing something wrong.
With a $5.4:1$ ratio of carbonated water to syrup, assuming that the quantities are additive (mixing 5.4 units of carbonated water with 1 unit of syrup yields 6.4 units of the mixture), I get: $$5\text{ gallons of syrup}\times\frac{6.4\text{ gallons of mixture}}{1\text{ gallon of syrup}}\times\frac{3.785\text{ liters}}{1\text{ gallon}}\approx 121\text{ liters of mixture}.$$ At $\$65$ per box, $$\frac{\$65}{121\text{ liters}}\approx\$0.54\text{ per liter}.$$ This is all ignoring the cost of carbonating the water, because around me, a 2-liter bottle of Coke goes on sale for 99 cents with enough regularity that it already doesn't make sense to mix at home.