Q.To use the Hungarian method, a profit maximization assignment problem requires ______.

The Hungarian method only solves minimisation assignment problems, so a maximisation (profit) problem must first be converted into a minimisation one — done by replacing each profit with its opportunity loss (largest element minus each element) — option (a).

The Hungarian method is designed to minimise total cost. When the assignment problem is one of maximising total profit, we cannot apply the method directly. We convert it into an equivalent minimisation problem: select the largest profit in the matrix and subtract every entry from it. The resulting entries are the opportunity losses (regret values); minimising total opportunity loss is equivalent to maximising total profit. The Hungarian steps (row reduction, column reduction, covering zeros with minimum lines, and optimal assignment) are then applied to this loss matrix.

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