To Develop Linear Programming (LP) Model to Determine the Best Combination or Mix of Products to Produce to Reach the Maximum Profit

Lending is a life wire or prominent business activity for banks. Loan portfolio therefore form a substantial amount of the assets of banks because it is the predominate source of interest income. The study was carried out to establish the impact of Linear programming model on the financial performance of banks, focusing on the Rural Bank X Lamashegu branch so that it can allocate funds to prospective loan seekers in order to maximize profits. To achieve this goal, a secondary data from the annual reports and financial statements were extracted for this study. Based on this data, LP model was formulated. A computerized software application called QM windows solver based on Revised Simplex Algorithm was used to solve the problem. The results from the model showed that Rural Bank X will be making annual profit of GH¢ 189144.14 from the amount GH ¢825812.77 invested on loan portfolio as against GH¢ 96879.00 in 2013 if the bank had the LP model in place. These product mix (ie. Midrofinance, Over draft and Commercial loans) were recommended for investment. The study also identified ineffective loan monitoring and poor credit vetting as the major factors accounting for some of the loan not performing in the loan portfolio, especially the Personal and Agricultural and Agro processing loans. Keywords: Loan portfolio, Linear programming, Simplex method, Bad debt and Over draf