Up until April 7, the men in the fort had access to supplies from Charleston, which one assumes would include food. So up until that point, the Confederates were making no effort to "starve them out".
Colonel L. THOMAS, Adjutant-General U. S. Army:
COLONEL: I have the honor to report that we do not see any work going on around us. There was more activity displayed by the guardboats last night than has been done for some time. Three of them remained, at anchor all night and until after reveille this morning, near the junction of the three channels. You will see by the inclosed letter, just received from Brigadier-General Beauregard that we shall not get any more supplies from the city of Charleston. I hope that they will continue to let us have our mails as long as we remain. I am glad to be enabled to report that there have been no new cases of dysentery, and that the sick-list only embraces six cases to-day.
I am, colonel, very respectfully, your obedient servant,
ROBERT ANDERSON,
Major, First Artillery, Commanding.
HEADQUARTERS OF THE PROVISIONAL ARMY, C. S., Charleston, S. C., April 7, 1861.
Major ROBERT ANDERSON,
Commanding at Fort Sumter, Charleston Harbor, S. C.:
SIR: In compliance with orders from the Confederate Government at Montgomery, I have the honor to inform you that, in consequence of the delays and apparent vacillations of the United States Government at Washington relative to the evacuation of Fort Sumter, no further communications for the purposes of supply with this city from the fort and with the fort from this city will be permitted from and after this day. The mails, however, will continue to be transmitted as heretofore, until further instructions from the Confederate Government.
I remain, sir, very respectfully, your obedient servant,
G. T. BEAUREGARD,
Anderson's March 1 report on supplies:
http://memory.loc.gov/mss/mal/mal1/076/0766400/001.jpg
"It will be seen, by the above, that there is flour and hard bread on hand, sufficient to sustain the whole command twenty eight days. "