# Linear Programming

Apr 30th, 2015
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The term ‛programming′ means planning and it refers to a particular plan of action amongst several alternatives for maximizing profit or minimizing cost etc. Programming problems deal with determining optimal allocation of limited resources to meet the given objectives, such as cost, maximum profit, highest margin or least time, when resources have alternative uses.

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linear programmingLinear ProgrammingLinear ProgrammingLearning Objectives:Introduction & Formulation of a Linear Programming Problem (LPP). Basic Concepts.Solution - Graphical solution and Solution through Excel Solver. Sensitivity Analysis.Linear ProgrammingIntroduction & Formulation of Linear Programming ProblemExample:A manufacturer can produce two products A & B.Unit ProfitLandLabor hourMachine hourARs.3501912BRs.3001616There are 200 units of land, 1566 hours of labor, and 2880machine hours available.Linear ProgrammingIntroduction & Formulation of Linear Programming PrbolemExample:ABRs.350Rs.300Land11Labor hour961216Unit ProfitMachine hourThere are 200 units of land, 1566hours of labor, and 2880 machinehours available.Quantity of A = X1 units &Quantity of B = X2 unitsMaxZ = 350X1 + 300X2Subject To1X1 + 15X2 2009X1 + 6X2 156612X1+16X2 2880X1 , X 2 0Linear ProgrammingIntroduction & Formulation of Linear Programming ProblemExample:MaxObjective FunctionZ = 350X1 + 300X2Subject To1X1 + 15X2 2009X1 + 6X2 156612X1+16X2 2880X1 , X 2 0ConstraintsNon NegativityConstraintsX1 & X2 are Decision VariablesLinear ProgrammingIntroduction & Formulation of Linear Programming ProblemLinear programming is a mathematical technique for determining the optimum allocation of resources to obtain a particular objective when the resources are

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