Mathematical optimization models have essential criteria for optimizing various industrial linear problems mainly involve the profit maximization or cost reduction. There are various significant mathematical models employed for solving budgetary linear programming in industries such as the Simplex and Interior Point Methods. In this study, two mathematical optimization models are developed namely Simplex Method (SM) and Interior Point Method (IPM) to solve linear programming problem. The objective function of linear programming model is to maximize the profit in food manufacturing company. By referring to the constraints that determined by the company in the aspect of production quantities, planned amount of profits and revenues, both models are developed to satisfy all constraints in order to obtain optimal nwnber of product quantities to be produced monthly. The products that been referred mainly come from six type of products namely, Red Beans (K₁), Green Beans (K₂), Chick Peas (K₃), Hamos (K₄), White Beans (K₅) and Large Beans (K₆) from LANA Company for Food Ltd for a period of 10 months in the year 2014. The results indicated that the IPM method produced optimal profit values than its
counterpart method and thus it's a promising optimization model for linear programming problem in industries.
