Alright, let's do the math then. 1/2 hour to burn a single body. A commonly reported statistic for Auschwitz is "~6000 jews per day".
I assuming this was true (for one, I suggest the Nazis could have been MUCH more efficient if that was their aim), and taking the 1/2 hour/body statistic;>pic related
6 bodies @ 1/2 hour/body = 12 bodies per hour per facility. 3 hours downtime puts the mass capacity at (12 bodies/hour * 21 hours of operation) 252 bodies/day, per facility (shown is a 6-oven configuration).
Link cites the commonly reported 6000/day figure for Auschwitz. Before taking that apart, let's use their own numbers.
6000/day, at 365/year, for 6 years (1940-45). We're using rough statistics for this one, because Auschwitz is said to only have operated from 1944-1945, but let's just play this out.
6000 * 365 * 5 = 13,141,000
Well THAT can't be right,....
So lets look deeper>Crematorium I operated [at Auschwitz] from August 15, 1940 until July 1943. According to calculations by the German authorities, 340 corpses could be burned every 24 hours after the installation of the three furnaces.
There's an evident variance of per day capacity, but let's run with it.
3 years at 340 people/day = 372,300>The Crematorium II building, which contained a gas chamber and furnaces for burning corpses. [...] According to calculations by the German authorities, 1,440 corpses could be burned in this crematorium every 24 hours. The gas chamber and Crematorium II functioned from March 1943 through November 1944.
Okay, so 21 months at 1,440 people per day we're throwing out the "prisoners say it could do much more" bit
puts Crema 2 at 1440 * 30 * 21 = 907,200.>The Crematorium III building, which contained a gas chamber and furnaces for burning corpses. [...] 1,440 corpses could be burned in this crematorium every 24 hours. According to the testimony of former prisoners, the figure was higher. The gas chamber and Crematorium III functioned from June 1943 through November 1944.
18 (months) * 30 (days) * 1440 (people) = 777,600>The Crematorium IV (and V) [...] 768 corpses (each) could be burned in this crematorium every 24 hours. March 1943 until October 7, 1944 (crema IV) and April 1943 until January 1945 (crema V)
So between the two, we have 1536/day, both operational for about 20 months (IV) and 22 months (V)
So for IV we have 768 * 30 * 20 = 460,800
And for V we have 768 * 30 * 22 = 506,880
Admitting these are extremely rough statistics:
I - 372,300
II - 907,200
III - 777,600
IV - 460,800
V - 506,880
Total - 3,024,780 Oy vey!
Here's an interesting resource you might like to see pertaining to myths and facts about WWII. I haven't read it in full, I was looking for statistics specific to gassings, but it presents a much more reasonable analysis of the situation.http://www.ihr.org/leaflets/auschwitz.shtml>Each year for decades, tens of thousands of visitors to Auschwitz have been shown an execution "gas chamber" in the main camp, supposedly in its "original state." In January 1995 the prestigious French weekly magazine L'Express acknowledged that "everything" about this "gas chamber" is "false," and that it is in fact a deceitful postwar reconstruction. 
I'm going to have to come back to this, its taken me an hour to compile and arrange all this. In the meantime, please note that crema 1 has 6 ovens, and crema 2 has 15. That will be important later. Also, if you or someone who speaks german could kindly pull up a map and point to the locations of crema 1-5, I would appreciate it.
[to be continued,...]