Linear programming, Production planning, Objective function, Mathematical model, maximize the profit, minimize the cost, optimal production mix, resources. 

Linear programming technique is one of the most important scientific progress since the mid-twentieth century, then the use of this technique is widespread in all sectors. Its application has increased lately because of technological progress that helped in the development of computers and software packages which can be used to solve linear programming problems after preparing the linear programming models to describe the relevant problem. Production planning is one of the most important fields where linear programming is used because of its ability to absorb all elements of the production process and to ensure that the available production elements are used optimally. Thus, this study is a practical application of linear programming technology in one of the Libyan industrial companies (Al-Aseel Food Industries Company), in order to get benefit from this technique in determining the optimal production mix of this company in accordance with the scientific methodology based on optimal allocation of economic resources. This study proves that the use of linear programming has a positive effect on improving production planning.