The Applications of Advanced Algebra in Linear Programming

Advanced Algebra is one of the basic core courses for all undergraduates in the department of mathematics.It is not only the extension of elementary mathematics,but also the foundation of Operations Research,especially of the Linear Programming.The knowledge of advanced algebra is used to solve the linear programming problem.Because the linear constraints of the standard format of the linear programming problem are the linear equations,the feasible solutions and the optimal solution are deduced from the point of view of the linear equations.According to the matrix form of the standard format of the linear programming problem,the expressions of the basic feasible solutions and the corresponding objective function value can be obtained,in addition to the criteria for the optimal solution.Moreover,the close relationship between the elementary transformation of the matrix and the simplex method is analyzed by the knowledge of the matrix.The correction of the above analysis can be illustrated by one typical example.