Okay, since you really can't seem to be arsed to put two and two together, I'm going to break this down one step at a time.
A diner costs 100 caps for 1 room, plus 25 caps for each additional room after that.
Ditto with a water treatment plant. Since the costs are the same, I'll be using the diner exclusively for cost calculation, multiplied by 2 where appropriate to account for having to build both.
To build a width 3 teir 1 diner costs 350 caps. To build two (to overtake the bottler's production advantage) costs 825 caps. Multiply that by two to account for 1650 caps total.
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A nuka cola plant costs 3000 caps, plus 750+ caps per room after the first. So 3000 for the first, 3750 for the second, and 4500 for the third.
3000+3750+4500= 11250. And we're not even talking upgrades yet.
That's 581% more expensive to build Three Bottlers than it is to build two diners and two water treatment plants!! And for only a 25% increase in production (something that's completely negated by using two of each)? And on top of that, building two diners and two water treatment plants grants 600 storage each. Building a bottler only grants 300 to both.
We haven't gotten very far and it's already not looking good, is it?
But hey, let's give the poor bottler a sporting chance here. I mean odds are you already have a diner or several and a water treatment or several. So for the sake of argument let's say... five 3width rooms of each. That's a total of 15 diners and 15 water treatments. Of course, no vault in their right mind would run that many, even at max capacity, but I'm feeling extremely generous. And let's say we want to build 2 more (since it would take 2 more to overtake the 25% increase production AND add 2x the storage of the bottler). Which would bring our total number of diners up to 21. (Again, insane. But we're being generous here.)
So the starting price is now 475. The next one would be 500, the next one after that 525, etc.
Which means: 475+500+525+550+575+600 = 3225 for both 3w rooms. Multiply that by 2 (to factor in the water treatment plant as well) and you get 6450 caps Total.
6450 caps for 6 Diner rooms and 6 Water Treatment rooms when there are already 15 of each as it is. Even with this insane handicap, Three bottler rooms is still 42% more expensive for a measly 25% production gain and a 50% storage loss to boot!
Even with a quite frankly ridiculous handycap, you can still get 12 rooms of those two cheaper than 3 of the bottler. And all you get out of the bottler is 25% more production value, which might I add is hardly worth it. Not to mention, yet again, you actually gain more out of the two 3x diners and 3x water treatments because you get twice as much storage out of them both.
Now, if you haven't thrown in the towel yet let's talk upgrades.
On a diner/WT, to upgrade to tier 2 is 500 caps. to upgrade to tier 3 from tier 2 is 1500 caps. 2000 caps total to upgrade from tier one to tier 3. 4000 caps total to upgrade both a diner and a water treatment plant. Times that by 2 to get 8000 caps needed to upgrade two 3wt1 diners and 2 3wt1 WTs to tier 3.
Add that to the cost of construction. 1650 + 8000 = 9650 ... yes, it costs 14% less to build two 3wt1 diners, two 3wt1 water treatment plants for four 3wt1 rooms total, and upgrade them all to tier 3, than it does to build one 3wt1 bottler.
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To add even more insult to the above, let's look a the bottler's upgrade cost.
15000 caps to upgrade a 3w room to tier 2. 45000 caps to upgrade to tier 3. For a total of 60000 caps.
Add that to the construction cost of 11250 caps, and your grand total comes to 71250 caps.
In closing: It is a whoping 638% more expensive to build and fully upgrade a single 3w bottler than it is to build two 3w diners and two 3w water treatments and upgrade all four of them to tier 3.
... and all this for less people (which you can make easily) and a 25% productivity increase (over one, not two) and no storage increase?!
?I'm sorry, but your math does not stack up. The cost vs gain does not stack up either.
Now, I'm sure you'll come up with some sort of excuse... IE that it costs more people (breed them and/or build more Barracks. Those are pretty cheap too btw.), costs more in power (power plants aren't expensive either, and if you're at this point you'll probably be running nukes anyway. 3 or 4 nuke reactors is enough capacity for even a 200 vault). But honestly, these are pretty weak excuses. Even if we factor in the cost of building another 3w3t barracks and power plant/nuke, it's going to end up pretty much the same way.
It's time to face the music, buddy: The bottler is overpriced garbage. Plain and simple.
... And don't even get me started on the Garden or Water Purifier.
You keep telling yourself that. For the rest of us, the math speaks for itself.
You keep using that word. I don't think it means what you think it means.