Artificial Insemination for a single woman

Q: If it permissible for a single woman, who is reaching the age of forty, sees that she does not have a reasonable chance of getting married and desperately wants a baby, to be artificially inseminated?
A: Artificial Insemination from a Jewish donor is impossible since the donation is made anonymously and since the father is unknown, there is a concern that the child will eventually marry one of his/her relatives.
Artificial Insemination from a non-Jew does not contain this problem. There are authorities (i.e. Ha-Rav Moshe Feinstein, Ha-Rav Shlomo Zalman Auerbach and others) who permit Artificial Insemination from a non-Jew for a married woman whose husband is infertile. From a certain perspective this is preferable to adopting a child, since at least the woman will be the child's natural mother.
In our case, however, it is improper since the child will be bereft of a father. It is true that there are single parents after a divorce or a death, and the child is bereft of a parent, but the child has a father. Our case is somewhat similar to a "shetuki" mentioned in the Gemara (Kiddushin 69a). A "shetuki" is someone who knows his mother but not his father, and he is called a "shetuki" because when he calls: "Abba," his mother says: "Shetok" (quiet). The Master of the Universe arranged that a child would have a mother and a father. This is normal. After the fact, a single mother can do a wonderful job raising children, but before the fact it is unethical for a mother to build her own happiness at the expense of the child. It will forever be difficult for him to respond to the question of who is his father, and it is possible that he will be suspected for being born out of wedlock in an illicit relationship.
Furthermore, it is possible that it is forbidden to have a medical procedure such as this. As is known, it is not obvious that medical procedures are permissible, and they are only allowed because the Torah explicitly permitted them: "And you shall surely heal" (Shemot 21:19) from which we learn that permission is given to a doctor to heal (Baba Kamma 85a). Hashem's will is for children to be born through the daughters of Israel from two parents who are married to one another, and not from a single woman. It is therefore possible that a medical procedure in order to impregnate a single woman is a Torah prohibition.
In sum: A single women should not be artificially inseminated and give birth to a child who will grow up without a father. Rather she should pray for Hashem's mercy to find the right mate to marry.