. Linear Programming Problem The Russian Mathematician L.V. Kantorovich applied mathematical model to solve linear programming problems. He pointed out in that many classes of problems which arise in production can be defined mathematically and therefore can be solved numerically.
This decision making technique was further developed by George B. Dantziz. He formulated the general linear programming problem - - Operations Research and developed simplex method ( ) to solve complex real time applications. Linear programming is one of the best optimization technique from theory, application and computation point of view.
Definition: Linear Programming Problem(LPP) is a mathematical technique which is used to optimize (maximize or minimize) the objective function with the limited resources. Mathematically, the general linear programming problem (LPP) may be stated as follows. Maximize or Minimize Z = … c x c x c x n n Subject to the conditions (constraints) a x a x n n $ q q n n $ q q … …. ….
… ... or m m mn n m $ q ……. x x $ Short form of LPP Maximize or Minimize Z = c x j j j