how long can a arleigh burke class ship operate before it has to restock food, soap ect.?

Answer 1

they generally can UNREP weekly, so they never really run out of everything at once.

Answer 2

On basic items such as food and supplies, a ship like that would be able to go for several weeks, but since it has to top off the fuel bunkers every week or so, they go ahead and load up then, along with spare parts and other necessities.

Answer 3

well they usually can last up to 45 days with out any outside assistance, also i wouldnt trust anything "fresh" (milk, fruits etc) after 15 days, link has alot of good info