In this paper, the authors are aimed at applying duality theory to multi-objective linear programming problems. Three methods of solutions were discussed and applied in this paper with the sole aim of finding out which of these three methods is the best for solving Multi Objective Linear Programming (MOLP) problems. The major components of the models used are the weighted sum and the e-constraint terms. Dual optimal functions were used in performing sensitivity analyses. The investigation in this paper was carried out using a bank’s investment data whose dual results showed that the merged weighted sum/e-constraint approach is the best method for handling MOLP problems.