Operational Research had its origins during the Second Word War as the result of the cooperation of scientists with senior officers of the Royal Air Force , to look into several military problems .
" In 1947, G . Dantzig developed an efficient method called , the simplex method, which can be used with the aid of the computer to solve linear programming problems even with thousands of constraints and thousands of variables in order to find their optimal solutions " [2] .
This research is aiming to revise comprehensively the procedure of Simplex method and to use the computer programme WINQSB in order to obtain the optimal decision to minimize the production cost for three different jackets models in Najaf Factory for Men Clothes .

Key Word : Linear Programing , Simplex , Minimization , Constrints , ObjectiveFunction , Optimal Sulotion ,Variables , Pivot Operation .