An Optimum Fund Allocation Pun from a Loan Portfolio: Case Study South Akim Rural Bank Limited

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The dissertation is designed to model a linear programming problem and apply optimization techniques to the operation of real life problems of banking given out loans to different clientele. The main objective of the study was to determine the maximum optimal profit which comprised the difference between the revenue from interest and the lost funds due to bad debts. Since bad debts are unrecoverable as both die principal and interest, thus reducing the total revenue. It is also used as the optimal solution to determine among the different clientele, the one that are recommended and those that are less attractive. A rural bank named, South Akim Rural Bank Limited was chosen for the case study. The bank gives loans to people of various categories, classified as Agriculture loans, Cottage industry loans, Transport loans, Commerce loans and Personal loans. The various group loans are analyzed and mdeled as various linear inequalities. Linear programming is developed and solved by using simplex tableau method It has found out that the bank made an optimal profit of 0.527192 million Ghana cedis annually with the decision variables optimal value: x, =0.0000, x2=0.0000, x3 =0.0000, x4 =0.9395and x5 =0.9400. This pilot study outlines the result of reduced Cost associated with some of decision variables and how to adjust them just to be profitable. ✓ Furthermore, the report looks at the effect analysis on the change of the Right-Hand Side of a constraint and that of the objective function coefficient for basic variables they have on the current basis, decision variables and the optimal Z-value 
A Thesis submitted to the Board of Graduate Studies in partial fulfillment of the Reqiurement for the Award of the Degree of Master Of Science (M.Sc) Industrial Mathematics, 2008