On a more serious note, I don't see how one can actually buy faster
single-core performance for this purpose.  If the question was more
detailed, describing specific models of machines, we'd be able to
show it makes no financial sense.  The cheapest stuff is good enough.

As I said before, I think information is getting lost here in the discussion. The issue is we need something that fits within certain restrictive thermal/size/power/noise limits; these are all fanless setups and some might even be battery powered. The sort of questions I'm facing are like do we go for a single core Celeron or a multicore Atom or what. I understand that the gross performance of a top of the line Xeon or whatever will make this issue moot, but we can't afford something like that for this project.

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