Why might a mathematician introduce a dummy variable to an algorithm?

Question

What is the purpose of dummy variables?  In solving problems apparently it is an arbitrary decision whether or not to introduce a dummy variable; so the mathematician must have a motive or a suspicion that the formulation without a dummy variable may be incomplete.

Answer 1

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.