This chapter explains how to solve the linear programming problem using the revised simplex method. It provides the steps for the revised simplex algorithm. The chapter suggests that if the simplex tableau A has fewer rows m than columns n, then in most instances, pivots occur in only a small fraction of the columns of the simplex tableau A. The operation of pivoting involves updating all the columns of the simplex tableau to move from one iteration to next in search of an improved solution. However, if a particular column of A never enters into basis during the entire simplex procedure, then computations performed on this column is not explicitly used. Therefore, the effort expended on performing operations on many such columns of A may be a waste. The revised simplex method reduces the amount of computation leading to an optimal solution by eliminating operations on columns of A that do not enter into the basis.