A mathemitician would do so because it states to in the algorithm. This is done in the simplex method in D1 to "pick up the slack" and another example of a dummy variable is in D2 in a non square array for the hungarian algorithm. How they work, i havent got a clue, it most likely allows for a lot more complex maths to be taking place, but the fact is they work. Put in dummy variables when it says, then take them out again once youve found your answer- thats it.