Drains are put in because the person undergoing the Whipple is having a fairly massive rearrangement of a number of organs of the digestive tract. That rearrangement necessitates suturing a large number of organs to each other to make sure that a person retains some functioning capability of the stomach, the pancreas, and the liver. During that procedure, some fluids can be 'lost' into the abdomen and while the 'adhesiveness' of the different organs starts to form at the suture lines, there can be leaks into the abdominal cavity. The fluids coming from the various organs that are sewn together are fairly caustic if they're loose in the abdomen and drains are needed to remove them - or to allow them a way to exit so they don't sit there and damage the surrounding tissues.
The drains will have to stay in until the docs and nurses are sure that any leaks have stopped and that you're not 'weeping' fluids from any intact organs.
The presence of a feeding tube may or may not be necessary depending of the type of Whipple that was done and the reaction