Technical note / Correction: The manuscripts have "mad'at al-dayf" (the invitation of the guest), but the most likely view is that this is an old tashif (copying error) and that the correct word is "mad'at al-da'if" (the invitation of the weak).
Note / Clarification: Its meaning is that the Prophet (peace and blessings be upon him) would accept the invitation to food of every weak person and slave. "Al-Mad'ah" refers to a banquet or the preparation of food.

Grading: This hadith is sahih, and this chain is "hasan" because of Muhammad bin al-Faraj al-Azraq; moreover, it has a corroboration (mutaba'ah).
Note / Clarification: Al-Hafiz Ibn Kathir declared it "jayyid" (good) in "al-Bidayah wa al-Nihayah" (8/484).

Reference / Source: Al-Bayhaqi narrated it in "al-Sunan", "Shu'ab al-Iman" and "Dala'il al-Nubuwwah" by way of Abu Abd Allah al-Hakim.
Technical note / Defect ('illah): In the printed "Dala'il al-Nubuwwah", the name of the Companion of the hadith, Abu Musa, has dropped out.

Reference / Source: Abu al-Shaykh ("Akhlaq al-Nabi (peace and blessings be upon him)"), al-Baghawi ("al-Anwar") and Ibn Asakir narrated it through two different routes from Shayban.

Note / Clarification: "Ya'taqil al-shah" means to milk a goat after pressing its leg between one's shin and thigh.
Important point: All these qualities are a great proof of the extreme humility and modesty of the Prophet (peace and blessings be upon him).