Verbal Model of an Assignment Problem

Say that the general assignment problem has n people and n tasks. Let cij represent the effectiveness if person I is assigned to task j. For the general assignment model, the objective is maximizing the total effectiveness of the assignments, i.e.:

maximize: total effectiveness of the assignments

subject to: number of tasks person i is assigned = 1 (i = 1 , . . . , n)
                  number of persons assigned to task j = 1 (j = 1 , . . . , n)