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From applications perspective, mathematical therefore linear programming optimization tool which allows rationalization many managerial technological decisions required contemporary techno socio economic applications important factor applicability mathematical programming methodology various application contexts computational tractability resulting analytical models under advent  modern computing technology tractability requirement translates existence effective efficient algorithmic procedures able provide systematic fast solution these models linear programming problems simplex algorithm discussed later text provides powerful computational tool able provide fast solutions very large-scale applications sometimes including hundreds thousands of variables decision factors fact simplex algorithm one first mathematical programming algorithms developed its subsequent successful implementation series applications significantly contributed acceptance broader field operations research scientific approach decision making

 

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