Discussion
The Hungarian method for the assignment problem is based on the fact that :
Answer: C
The Hungarian method rests on the fact that the optimal assignment is not affected by adding or subtracting a constant from any row or column.
Adding or subtracting a constant from every entry of a row (or column) changes the cost of every complete assignment by exactly that constant, because every assignment uses exactly one cell in each row and column. The ranking of assignments, and so the optimum, stays the same. The method uses this to reduce rows and columns until enough zeros appear.
Option A states only the subtraction half of the theorem. Option B is wrong because the objective value does change, by the constant. Option D misdescribes the procedure: entries are reduced row by row and column by column, not one at a time.
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