I will link you to an older post of mine on the evolution of the Holocaust and will say that initially forced emigration was the policy the Nazi pursued but there were two factors that lead to the radicalization of Nazi policy: The state of the war that made emigration immensely difficult both logistically as well as politically and then the attack on the Soviet Union. Palestine was not an option because that was territory the Germans still intended to conquer and bring under their control at some point and because the British had – as is usual in wars – travel restrictions in place.

It seems that in this question you are considering "utilitarian" as cheapest, however you may want to reflect on whether what you know about the holocaust actually shows the sort of thinking you suggest.

For example the holocaust created a vast slave workforce. Does your understanding suggest that the slave workforce was treated rationally to maximise their productivity to the nazi regime ? Or, were they treated in such a way that they were effectively being punished for being Jewish by being worked to death ? If you accept that the second view prevailed then the concept of utilitarianism overriding racial ideology recedes.