Natural SciencesMathematicsMathematical EconomicsOptimizationSchedulingConstrained OptimizationCost MinimizationLinear ProgrammingMathematical ProgrammingOptimization In EconomicsOptimization TheoryLinear Cost FunctionsProblem Statement FormulationScheduling Problems
Introduction 1.1 Definition Linear programming is the name of a branch of applied mathematics that deals with solving optimization problems of a particular form. Linear programming problems consist of a linear cost function (consisting of a certain number of variables) which is to be minimized or maximized subject to a certain number of constraints. The constraints are linear inequalities of the variables used in the cost function. The cost function is also sometimes called the objective function. Linear programming is closely related to linear algebra; the most noticeable difference is that linear programming often uses inequalities in the problem statement rather than equalities. 1.2 History Linear programming is a relatively young mathematical discipline, dating from the invention of the simplex method by G. B. Dantzig in 1947. Historically, development in linear programming i