operational research<\/a> technique) designs to solve allocation problem. <\/p>\n\n\n\nThe term \u2018linear programming\u2019\nconsists of the two words \u2018Linear\u2019 and \u2018Programming\u2019. The word \u2018Linear\u2019 is used\nto describe the relationship between decision variables, which are directly\nproportional. For example, if doubling (or tripling) the production of a\nproduct will exactly double (or triple) the profit and required resources, then\nit is linear relationship. The word \u2018programming\u2019 means planning of activities\nin a manner that achieves some \u2018optimal\u2019 result with available resources. A\nprogramme is \u2018optimal\u2019 if it maximises or minimises some measure or criterion\nof effectiveness such as profit, contribution (i.e. sales-variable cost),\nsales, and cost. <\/p>\n\n\n\n
Thus, \u2018Linear Programming\u2019\nindicates the planning of decision variables, which are directly proportional,\nto achieve the \u2018optimal\u2019 result considering the limitations within which the\nproblem is to be solved.<\/p>\n\n\n\n
ACCORDING TO WILLIAM M. FOX<\/strong><\/p>\n\n\n\n\u201cLinear\nprogramming is a planning technique that permits some objective function to be\nminimized or maximized within the framework of given situational restrictions.\u201d<\/p>\n\n\n\n
HISTORICAL BACKGROUND<\/strong><\/p>\n\n\n\nThe technique of\nlinear programming was formulated by a Russian mathematician L.V. Kantorovich.\nBut the present version of simplex method was developed by Geoge B. Dentzig in\n1947. Linear programming (LP) is an important technique of operations research\ndeveloped for optimum utilization of resources.<\/p>\n\n\n\n