Tuesday, September 23, 2008

Linear programming

Decision making has always been very important in the business and industry world . A production manager is always thinking about the commodities to be produced and the quantities of each commodity to be produced . He is also very particular on the processes to be applied . Alfred marshall feels that the businessman by his trained instinct rather that with formal calculations tries to minimize the cost function . But now there does exist a method of formal calculations often termed as linear programming . Russin mathematician Mr. L.V. Kantorovich was the first to formulate this method . But in 1947 George B. Dantzig developed it for the purpose of scheduling the complicated procurement activities of the united states air force.

Today this method is being used in solving most of business problems . Electronic computers have increased its applications to solve many other problems in industry.

Meaning of linear programming
The word linear means that the relationship handled are those represented by straight lines , the relationships are of the form y = mx +c and the word programming means taking decisions systematically .Thus linear programming is decision making technique under given constraints on the assumption that the relationships amongst the variables representing different phenomena happen to be linear . In other words,” linear programming is the maximization or minimization of a linear function of variables subject to a constraint of linear inequalities .”
In simple words , linear programming is a mathematical technique for finding the optimum solution to a linear function of two or more decision variables subject to a set of linear constraints .The linear function to be optimized is called the objective function .
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