Being based on the theoretical considerations presented in part I a general solution procedure is given, which during the process uses basic solutions with negative components, too. Criteria for the variables which have to enter the basis solution and for those which have to leave it are proposed. Hereby the value of the discrepancy does not increase. The first basis solution   with   is discussed. The case, in which the objective function is unbounded over the feasible region is considered in details. Then by specification the primal-dual algorithm and a primal simplex method are developed from the general solution procedure.