Modified Algorithms for Solving Linear Programming Problems

              In   this   work,   we   studied    the   ``Path-Following  Algorithm``,  which  is  one  of  the  family  algorithms, called ``Interior-Point   Algorithms``. We   are   discussed   two   modifications,    the   first
one concerned   with  the  path  solution,  while  the   second one   is concerned    with     the    feasibility   solution.  These two    modifications   are  combined   in  a   new   manner,  to construct  a  hybrid   method. The   same  test  problem  had been   run   for all  the   algorithms,  as  well  as,  number   of tested   problems   had    been implemented  for comparison, shown  that  our   modifications   give  better   results  in   the number of  iterations  and  the   accuracy  of   the  results.