Application of Linear Programming Model for Optimal Production Planning: A Case Study of Adama Beverages, Jimeta Yola, Adamawa State, Nigeria

Abstract

The Linear Programming Problem (LPP) as an applied mathematical model has been applied in business related problem for optimization purposes (maximizing profit or minimizing cost of production). This study applied linear programming model as an optimal model on the production planning for the maximization of profit in Adama Beverages, Jimeta Yola, Adamawa State Nigeria. We adopted exploratory research designed because the study was designed in order to determine 750ml of bottle water, 1000ml of fruit juice and 250ml of sachet water that a company can produce on a weekly basis in order to maximize profit and minimize production cost given the quantity of each resource consumed by each product. The data for the study were secondary data collected from the company. The variables of the study were the concentrate, sugar, distilled water of the precise quantity often used by the firm and flavour. These data were formulated into the linear programming model and analyzed using Temporary Ordered Routine Algorithm (TORA) software. The optimal tableaus of the TORA iterations were obtained in Iteration four (4).  The results revealed that the company should produce 571 quantities of bottle water (X₁) and 2,143 quantities of fruit juice (X₃) on a weekly basis in order to yield weekly profit of  Z^* = N835,714.29k  while neglecting the production of sachet water as it profit contribution is 0 (X₂). We recommend that the company should produce above quantities of bottle water and fruit juice in order to gain much profit.