When something exhausts you, it uses up all of your energy, leaving you feeling very tired. And when you exhaust your supply of something, you use up every bit of it, and it's gone. To be exhausted is to be extremely worn-out, tired, or sleepy--or just very bored and very done with whatever you're doing.
George Michael feels so exhausted that he lies down on the floor. He really needs to rest! His energy is completely gone.
If you've exhausted your supply of food, you don't have any food left at all. To exhaust something is to use all of it.