Wasn’t there a particularly heated SDMB thread a while back, maybe a year, about what you’d do if there was one woman left on Earth and she didn’t particularly feel like continuing the species? I seem to recall it giving me bad dreams. As in that thread and in this scenario, as phouka pointed out, you have to wonder what kind of life this women and any of her daughters would be living. When humanity’s existence hangs in the balance you probably don’t get much of a life. And what a mothering experience, knowing people are waiting in line for your daughter’s first period so she can join the cause. Because of what would have to be done, and with our track record, humanity might not be worth saving.
What does she look like?
There is only one women right? But all the doctors didn’t die right? So The said women will have to have at least triplets each birth. And even more so the doctor can control the sex of the babies to some extent if I’m not mistaken. So if she is 22. She can have many children before she is too old or it is unsafe for her to have kids but if it is for human kind I guess she would risk her life to save us.
Triplets have a five to tenfold risk of death in the first week after death. 87 to over 90% (depending on the study and country) of triplets are premature, compared to 8% for singletons and 28% of very premature (born before 33 weeks) infants are triplets. Maternal high blood pressure and preeclampsia are much higher in triplet pregnancies.
In short, you’re betting high stakes and high risks using a multiple strategy. I’d save it for later in her life when, oddly enough, the risks of and to triplets, especially those conceived through IVF and not spontaneously, actually goes down.
A woman who just had sex is the minimum that is required 
There was a really well-done comic book, “Y: The Last Man,” that dealt with more-or-less this premise. (Except, of course, that there was only one man left, rather than one woman.) He … doesn’t have a good time of it, to put things mildly. For starters, he’s the series makes it pretty clear that he will never, ever have anything like you or I would consider “freedom”.
What could be better then death by snu snu?
lets just say, everyone is free of sexual disease, and everyone wants to repopulate. for example i’m just going to say there is 10 guys.
Lets say that the only female is 13, and all fertile guys are 13. and they decide all generations must start mating at 13.
A female child born of the original girl could have children with 9 men she’s not related to. her children could mate with 8 of the original men. and so on. if everything went to plan, this could reasonably go on for three generations, just with the original guys (Which would make the original guys around 52) this would mean the incest would be a bit removed, grandparents/great grandparents being related
It would be really helpful if all children that were born in the first generation were female. improbable, but possible.
Assuming everyone is really fertile and healthy, i could see they working. I’m a bit tired, so I can’t be bothered in really figuring this out, there might be a problem im not seeing with this.
With modern technology, is it possible to grow a human embryo in a non-human uterus? There could still be thousands of female apes in the world.
I would say it’s best that she’s not monogamous. There’s no shortage of men so why not allocate, say, 10 men at first. It will increase the chances of her getting pregnany more quickly. When she gets pregnant, those 10 men have cough ‘had their turn’ and a different 10 men are allocated for the next time.
It would be very tiring for the woman (70 times a week would tire anyone out) but would improve humanitys chances.
It would help if the woman had an exceptionally high sex drive and low standards.
Oh Octomom, we need you!
I liked that series a lot, but I felt that the last volume was wrapped up much too quickly.
As for the OP, if we assume that the woman is capable of multiple egg donations, then that’s the way to go. Have her go through a few cycles of multiple egg collections, fertilize them, and freeze most of them. Freeze a lot of sperm samples from the guys, too. Let her recover from the egg donations, and implant two female zygotes (I assume that it’s fairly easy to tell male from female zygotes). But these zygotes should be from different fathers. Lather, rinse, repeat, with different fathers each time. She shouldn’t get pregnant more than once every two or three years, because of she’ll need time to recover. The fathers take care of the infants, preferably with help from other men as well. Her daughters will also probably have to bear only daughters, at least at first. We’re not destroying the male zygotes, they’re still in the deep freeze. If possible, some of the men should have zygotes implanted, too.
A big problem here is that the culture is going to be very out-of-whack because the girls are going to be growing up without boys their own age to interact with. I have a brother, and when I was growing up, my best friends were usually boys. So we might consider implanting one male to every three or four females, to try to keep it from getting too lopsided.