LLLLiiiinnnneeeeaaaarrrr    PPPPrrrrooooggggrrrraaaammmmmmmmiiiinnnngggg
         th
        6 LOE (UNIT 1)
        Mechanical  Dept, NIT Srinagar 
        CCoouurrssee    IInn  cchhaarrggee
        SAAD PARVEZ
        MMoodduullee  OOuuttlliinnee
     Introduction
     The Linear Programming Model
     Examples of Linear Programming Problems 
     Developing Linear Programming Models
     Graphical Solution to LP Problems
      TThhee  SSiimmpplleexx  MMeetthhoodd
     Simplex Tableau for Maximization Problem
     Marginal Values of Additional Resources
     Sensitivity Analysis
     Complications in Applying the Simplex Method
     Duality
         IInnttrroodduuccttiioonn  
    Mathematical programming is used to find the best or optimal
     solution to a problem that requires a decision or set of
     decisions about how best to use a set of limited resources to
     achieve a state goal of objectives.
    Stepsinvolvedinmathematicalprogramming
      Conversion of stated problem into a mathematical model that
       abstracts all the essential elements of the problem.
      Exploration of different solutions of the problem.
      Findingoutthemostsuitable or optimum solution.
    Linear programming requires that all the mathematical
     functions in the model be linear functions.
                                                           TThhee  LLiinneeaarr  PPrrooggrraammmmiinngg  MMooddeell  ((11))  
                             Let:                    X , X , X , ………, X = decision variables
                                                         1          2         3                                  n
                                                     Z=Objectivefunction or linear function
                             Requirement: Maximization of the linear function Z.
                                                     Z=cX +cX +cX +………+cX                                                                                                                            …..Eq(1)
                                                                       1 1                     2 2                     3 3                                                     n n
                                         subject to the following constraints:
                                                                                                                                                                                                     …..Eq (2)
                               where a , b, and c are given constants.
                                                       ij       i                    j