The chest containing the supplies you should find in the room at the back. The room is containing two chests, one just behind the iron gate at the right wall, the other one at the end of the room. If I remember right, it should be the chest on the right.
This
map isn't very detailed, but at least confirming the position in the back room.
milorien
Edit: To make sure I was right, I just loaded a save and checked the map. So - the position of alutiq on the linked map is completely worng. You'll find him and the chest with Wesson's supplies in the north of the mine. On the linked map it's the spot numbered with a yellow
3. Sorry for recklessly linking the map.
