The Vedanta Sutras of Badarayana, Commentary by Sankara (SBE38), tr. by George Thibaut  at sacred-texts.com
41. When (eating) is taking place, (the prânâgnihotra has to be performed) from that (i.e. the food first eaten); on the ground of the passage declaring this.
When eating is actually taking place, 'from that,' i.e. with that material of food which first presents itself, the agnihotra offered to the prânas is to be effected.--On what
ground?--' On the ground of the passage declaring this.' For the clause, 'The first food which a man may take is in the place of a homa,' enjoins the circumstance of the oblations to the prânas being effected by means of a material (primarily) subserving another purpose (viz. eating), as appears from its referring to the presentation of food as something accomplished (i.e. accomplished independently of the oblations; not tending to accomplish the oblations). How then should these oblations--which are characterised as not having any motive power with regard to the employment of the food--be capable of causing us to substitute, in the absence of eating, some other material (than food)?--Nor is it true that there are already established, for the prânâgnihotra, all the details belonging to the fundamental agnihotra. In the case of the ayana of the Kundapâyins, the term 'agnihotra' forms part of the injunctive passage, 'They offer the agnihotra during a month,' and therefore may have the force of enjoining a general character of the sacrifice identical with that of the fundamental agnihotra; and it is therefore appropriate to consider the details of the latter as valid for the agnihotra of the Kundapâyins also. In the case of the so-called prânâgnihotra, on the other hand, the term 'agnihotra' occurs in an arthavâda-passage only, and does not therefore possess an analogous injunctive force. If, again, we admitted that the details of the fundamental agnihotra are valid for the prânâgnihotra also, such details as the transference of the fire (from the gârhapatya fire to the two other fires) would be likewise valid. But this is impossible, as the transference of the fire is made for the purpose of establishing a fireplace in which the oblations are made; in our case, on the other hand, the oblations are not made in the fire at all--because that would interfere with their being used as food, and because they are connected with a material procured for the purpose of eating,--but are made in the mouth (of the eater). Thus the text of the Gâbâlas also, 'He is to eat before the guests,' shows that the accomplishment of the oblation has the mouth for its abode. For the same reason (i.e. because the details of the fundamental agnihotra are
not valid for the prânâgnihotra) the text declares the subordinate members of the agnihotra to be present here (i.e. in the prânâgnihotra) in the way of fanciful combination only, 'the chest is the vedi, the hairs the sacrificial grass, the heart the Gârhapatya fire, the mind the Anvâhâryapakana fire, the mouth the Âhavanîya fire.' By the vedi mentioned in this passage we have to understand a levelled spot, as in the fundamental agnihotra there is no vedi, and as the intention of the passage is to effect a fanciful combination of the members of the fundamental agnihotra (with members of the prânâgnihotra).--And as the prânâgnihotra is connected with eating which has its definite times, it is also not possible that it should be restricted to the time enjoined for the fundamental agnihotra. In the same way other particulars also of the fundamental agnihotra, such as the so-called upasthâna, cannot be reconciled with the requirements of the prânâgnihotra. From all this it follows that the five oblations, as connected with their respective mantras, materials, and divinities, have to be performed only in the case of food being eaten.--With reference to the passage showing 'respect,' we remark that it is meant to intimate priority (of the host), in the case of food being actually eaten. But the passage has no power to declare that the offering of the prânâgnihotra is of permanent obligation.--It therefore is a settled conclusion that the prânâgnihotra is omitted when the eating of food is omitted.