Abstract

Abstract:
The objective of this thesis is to study and development the solution of linear programming problems with free variables. This thesis studied number of methods with its algorithms to solve the above problems. The thesis studied one of classical methods which expressed any free variable as a difference between two nonnegative variables, then the modified MPS method is studied which expressed any free variables as a function of remaining nonnegative variables . It is found that MPS method is better than classical method, since MPS method reduced the tables number, make the calculations easier and reduced the solution time. Also MPS method used some basic theorems to determine the solution result for some problems from the initial table with out depending on the problem detail solution . This thesis also includes appendix represented the package programs with Visual Basic language (Microsoft Visual Basic 6.0), to get a good forms of display at execution and solving all the problems that may be found in this scope to apply all methods that included in this thesis