Linear Programming

May 5th, 2015
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Linear programming problems A linear programming problem in two unknowns x and y is the problem in which we are to find the maximum or minimum value of a linear objective function P = ax + by subject to a number of linear constraints cx + dy ≤ e or cx + dy ≥ e or cx + dy = e where a, b, c, d, and e are real numbers.

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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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