## ABSTRACT

This chapter discusses the importance of basic feasible solutions in solving linear programming problems. The fundamental theorem of a linear programming problem was proved to solve the problems. The aim of the simplex algorithm is to move from one basic feasible solution to another until an optimal basic feasible solution is found and the value of objective function continually decreases until a minimum is reached. A basic feasible solution is optimal if and only if the corresponding reduced cost coefficients are all non-negative. A basic feasible solution is optimal if and only if the corresponding reduced cost coefficients are all non-negative. The set of feasible solutions of a standard form linear programming problem is a convex set. If there exists a feasible solution, then there exists a basic feasible solution and if there exists an optimal feasible solution, then there exists an optimal basic feasible solution.