The Graphical Method for Finding the Optimal Solution for Neutrosophic linear Models and Taking Advantage of Non-Negativity Constraints to Find the Optimal Solution for Some Neutrosophic linear Models in Which the Number of Unknowns is More than Three

Abstract

The linear programming method is one of the important methods of operations research that
has been used to address many practical issues and provided optimal solutions for many
institutions and companies, which helped decision makers make ideal decisions through
which companies and institutions achieved maximum profit, but these solutions remain
ideal and appropriate in If the conditions surrounding the work environment are stable,
because any change in the data provided will affect the optimal solution and to avoid losses
and achieve maximum profit, we have, in previous research, reformulated the linear models
using the concepts of neutrosophic science, the science that takes into account the
instability of conditions and fluctuations in the work environment and leaves nothing to
chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin
of freedom to decision makers. In another research, we reformulated one of the most
important methods used to solve linear models, which is the simplex method, using the
concepts of this science, and as a continuation of what we did in the previous two
researches, we will reformulate in this research. The graphical method for solving linear
models using the concepts of neutrosophics. We will also shed light on a case that is rarely
mentioned in most operations research references, which is that when the difference
between the number of unknowns and the number of constraints is equal to one, two, or
three, we can also find the optimal solution graphically for some linear models. This is
done by taking advantage of the conditions of non-negativity that linear models have, and
we will explain this through an example in which the difference is equal to two. Also,
through examples, we will explain the difference between using classical values and
neutrosophic values and the extent of this’s impact on the optimal solution.