Neutrosophic Handling of the Simplex Direct Algorithm to Define the Optimal Solution in Linear Programming

Mathematical programming has the ability to express competency concepts in a well-defined mathematical model for a particular situation or system, and the ability to derive computational methods to solve this mathematical model, it is also a mathematical tool that allows us to model, analyze and solve a wide range of problems concerned with allocating rare resources of labor, materials, machinery, and capitals. Consequently, using them in the best attainable way in order to minimize costs or maximize profits. In such issues, the linear programming is one of the most widely used types of mathematical programming because it is a method that helps to make good decisions and decide the best program for independent activities, taking into account the available sources. It does not take in consideration the continuous and rapid changes and the state of instability in data. So, this manuscript studies one of the methods to solve linear models, which is the simplex method using the neutrosophic theory that covers all the data in analysing, whether specific or not, determined or not, having consistency or not, as well as it deeming all occurring changes. However, the optimal solution is related to the variables in the objective function, which in turn are affected by the fixed quantities that express the available possibilities. This article presents a study to solve the linear model using the simplex method in which the variables and their coefficients are indeterminate values, and we will explain the effected of the indeterminate values on the optimal solution of the mathematical model. The product mixture problem has been presented as case study to demonstrate the efficiency of the proposed method.