From a strictly grammatical point of view, you are right. "without which yeast can do" is a correct way of saying this. However, it is an awkward construction because it is not the way people talk and this is, after all, part of a conversation. I think that what may be causing you to question the author's construction is the "rule" about not ending a sentence or clause with a preposition, but in this situation we have a phrase "do without" which is commonly used in English and means to go along in life without something and usually implies that the "something" is disireable, but not absolutely necessary. So, in this case, *do without* needs to stay connected. That leaves the question of the word *with*. It is not necessary. The clause could also have been written, "which yeast can do without." The answer is that authors often use a certain amount of "poetic license" in constructing their sentences and Asimov might have liked the rhythm of the words the way he wrote the sentence.

Thank your for your explanation. What struck me about this sentence was the inclusion of the word "with" which seems to contradict the "without" at the end. I take it for poetic license now.