Before a more qualified (and educated/trained) Historian marvels us with their contribution I'll just drop down some points from what I understand regarding this topic.

Firstly, I believe the Holocaust and the 'Final Solution' are two slightly different terms, the Holocaust being the over-arching systematic imprisonment and forced labor of 'undesirables' in concentration and work camps, and the Final Solution being the last ditch effort by the Nazi Party to fully kill off the undesirables and more or less cover up evidence from the approaching Allied armies.

Having that out of the way, Germany's war effort was both hindered and run by concentration and work camps. Slave labor was tremendously vital to the German military complex during the war and helped keep costs production costs low and turnout high (as well as keeping the homefront happy which was one of Hitlers intense goals after what happened in WW1). Many undesirables with crafts and skills were pressed into service all over the Nazi controlled territories but some have attributed the forced labor to low quality products being turned out (why put in serious effort to help create killing machines for your tormentors outside of the threat of death when you were miserable anyway).

Perhaps more surprising and hypocritical was the Nazi practise of extracting blood from Jewish prisoners for use in field hospitals for German soldiers which I've always thought was particularly interesting.

I've realized through reading over my answer that it's a bit muddled/not very professional so my apoligies for that! If I had to summarize it: The Holocaust was vital to economic viability of Nazi Germany's war making with the rest of Europe whereas the Final solution was largely an attempt to free up resources being used to house undesirables and hide evidence that could be used as propaganda against them.

Source: General knowledge, but more specifically Michael Thad Allens 'The Business of Genocide: The SS, Slave Labor, and the Concentration Camps'