Gemara

Question: If (Nochri) soldiers demand that Yisraelim in a valley cook for them on Yom Tov, is this permitted?

Answer (Rav Huna): It is permitted only if they would not mind if we gave (some) to a child, for then each loaf is fitting for a child.

Question (Beraisa) Shimon ha'Temani said that soldiers once came to his city on Yom Tov and sought to seize all the food. The Yisraelim slaughtered a calf for them and fed them, and they left.

R. Yehudah ben Bava: You erred! You may cook "Lachem", but not for Nochrim.

Summation of question: It is not permitted, even though Yisraelim could also eat from it!

Answer (Rav Yosef): The calf was Tereifah.

Question: Dogs (of the Yisraelim) could eat from the calf!

Answer: Tana'im (explicitly) argue about whether or not we may do Melachah for Ochel Nefesh for animals (so it is reasonable to say that R. Yehudah ben Bava forbids and Shimon ha'Temani permits):

(Beraisa - R. Yosi ha'Gelili) Suggestion: Perhaps Meleches Ochel Nefesh is permitted even for animals, for they are called "Nefesh Behemah"!

Rejection: It is permitted "Lachem", but not for dogs.

R. Akiva says, it is permitted even for animals. "Lachem" forbids for Nochrim.

It is more reasonable to permit for dogs, for we must feed our animals, but we need not feed Nochrim.

Question (Abaye): According to R. Yosi ha'Gelili who forbids Meleches Ochel Nefesh for animals, why may we throw date pits to animals on Yom Tov? (The pits are Muktzah!)

Answer (Rav Yosef): They are not Muktzah. They can be burned for fuel.

Question (Abaye): Why is it permitted on Shabbos?

Answer (Rav Yosef): One moves them via bread.

He (Rav Huna) argues with R. Yehoshua ben Levi:

(R. Yehoshua ben Levi): One may invite a Nochri to come to eat on Shabbos, but not on Yom Tov. This is a decree lest he cook extra for the Nochri.

Rishonim

Rif and Rosh (2:14): The Halachah does not follow Rav (Huna, who permits to cook for soldiers on Yom Tov we could gave some to a child), because R. Yehoshua ben Levi forbids inviting a Nochri on Yom Tov, lest he cook extra for him.

Question: Nowadays, we feed our slaves on Yom Tov. Why is this permitted?

Answer #1 (Ran, ibid.): We are concerned only when one invites a Nochri, for then one is wont to show honor to him. However, it seems that one may not make extra bread for him.

Answer #2 (cited by Ran, and R. Shavat cited in Hagahos Maimoniyos Hilchos Yom Tov 1:9): We may cook extra for our slaves, or even for Nochrim accompanying us on the road, for we are obligated to feed them. This is like R. Akiva, who permits Meleches Ochel Nefesh for animals because we must feed them. This is unlike the Rif, who rules like R. Yosi ha'Gelili.

Answer #3 (Hagahos Maimoniyos, ibid.): Our slaves are satisfied with other things. (Whatever we cook for them we could eat ourselves, for we could give to them other food.)

Rambam (Hilchos Yom Tov 1:13): One may not bake or cook on Yom Tov for Nochrim or dogs. "Hu Levado Ye'aseh Lachem" - not for Nochrim or dogs. One may not invite a Nochri to come to eat on Yom Tov.

Rambam (14): If (Nochri) soldiers gave flour to Yisraelim to make bread for them on Yom Tov, we may do so only if they would not mind if we gave a loaf to children, for then each loaf could be for a child.

Ra'avad: This is correct, even though it is unlike the Rif.

Question: How can the Rambam rule like Rav Huna and (in Halachah 13) like R. Yehoshua ben Levi? The Gemara said that they argue!

Answer #1 (Ran DH v'Havi): The Rambam's text did not say that they argue. He explains that Rav Huna permits when we could not give to a child unless we bake all of the loaves, therefore all the baking is necessary for the Yisrael.

Answer #2 (Magid Mishnah): The Rambam had our text. It says 'he argues with R. Yehoshua ben Levi.' The Rif and Rashi explain that this refers to Rav Huna. The Rambam disagrees, for they discuss different matters. Rather, 'he' refers to the last opinion, Rav Yosef, who says that when Meleches Ochel Nefesh is forbidden on Yom Tov (e.g. for animals), we may not move Muktzah on Shabbos. This is unlike R. Yehoshua ben Levi, who forbids Meleches Ochel Nefesh for Nochrim on Yom Tov, but permits to invite and feed Nochrim on Shabbos (even though he will refill their cups and move leftover wine in the cups, which is Muktzah). The Ra'avad agreed with this.

Kesef Mishneh: The Ra'avad said that the Rambam is unlike the Rif. Surely the Rif agrees that we may bake all of the loaves if otherwise we cannot give to a child! Perhaps the Magid Mishnah understands the Ra'avad to say that the Rif explains differently (who argues with R. Yehoshua ben Levi), but not that they argue about the Halachah.

Answer #3 (Migdal Oz): One may not willingly invite a Nochri. The valley is obligated to feed the soldiers, therefore (when a child may have some) it is permitted, like bread that is primarily for dogs but also shepherds can eat it (21a).

Rosh (2:14): If a Nochri messenger came to a Yisrael's house, he may give to him to eat. Likewise, in Ashkenaz people have Nochri slaves (and they feed them on Yom Tov). We are not concerned lest one cook a pot just for his slave. One may add to the pot he cooks for himself.

Poskim

Rema (OC 512:1): One may cook extra for his slave in the same pot he cooks for himself.

Mishnah Berurah (11): The Mechaber equated slaves and Nochrim. The Rema distinguishes them, and permits cooking in the same pot for an Eved Kena'ani. One may not explicitly say that he adds for him.

Mishnah Berurah (12): One who bakes toils individually for each loaf. Therefore, one may not bake for slaves unless they could be appeased with other food (and Yisraelim would eat all the loaves). This applies to small ovens in which the dough is stuck to the walls; the bread bakes better when the oven is full. It does not apply to our ovens, so we should bake only what Yisraelim will eat. In pressed circumstances one may be lenient even with our ovens.

Kaf ha'Chayim (21): One may not add to the pot for the need of slaves once it is on the fire. Even though one may add to eat after Yom Tov, this is only if Yisraelim could eat everything on Yom Tov if they wanted. This is not so here, for he must feed his slaves. If he could satisfy them with other food it is permitted.

Shulchan Aruch (2): If Nochri soldiers gave flour to Yisraelim to make bread for them on Yom Tov, we may do so only if they would not mind if we gave a loaf to children, for then each loaf could be for a child.

Question (Olas Shabbos, brought in Kaf ha'Chayim 26): Why does the Shulchan Aruch rule like the Rambam against the Rif and Rosh?

Answer (Ma'amar Mordechai): The Beis Yosef explained that the Nochrim allow us to give to a child only if we bake all their flour. The Rif agrees in such a case.

Mishnah Berurah (13): Some say that we must give some to children. It is not enough that we could.

Taz (6): If the flour was of the Yisraelim, they could bake as they pleased for children. If so, there would be no Heter to bake for Nochrim just because this enables us to give some to children!

Mishnah Berurah (15): One should rely on the Heter of giving some to a child only in pressed circumstances.