aspg-24-1926-1791482519 20261008180159 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2023 6 2 Maissam Jdid Faculty of Informatics Engineering, Al-Sham Private University, Damascus, Syria Linear programming problems with integers, are issues in which some or all decision variables are restricted to be their values are correct values, and here these models can be solved by neglecting the constraints of integers and then rotating the fractional values of the optimal solution to obtain correct values, paying attention to the need for the resulting solution to belong to the accepted solutions area, but this procedure can lead to the desired purpose if the number of variables is small, but if there is a number We do not guarantee to obtain an optimal correct solution for the model, even if all the solution combinations are tested, knowing that in the model that contains a variable n a set of solutions 2n must be tried, and if we can rotate, the correct solution will be an approximate solution, in order to obtain more accurate integer values, we present in this research a study in which we use binary integer variables to build the neutrosophic linear mathematical model. The importance of this study lies in providing solutions to many practical problems that require solutions with integers and we will clarify all the above by building a mathematical model for the problem of the mixture of products using binary integer variables and neutrosophic values. 2023 55 58 1926 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.060206 https://www.americaspg.com/journal/24/article/1926 https://www.americaspg.com/storage/91688735284.pdf