Transcription of 9.3 THE SIMPLEX METHOD: MAXIMIZATION
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9.3 THE SIMPLEX METHOD: MAXIMIZATION
THE SIMPLEX METHOD: MAXIMIZATIONFor linear programming problems involving two variables, the graphical solution methodintroduced in Section is convenient. However, for problems involving more than twovariables or problems involving a large number of constraints, it is better to use solutionmethods that are adaptable to computers. One such method is called the SIMPLEX method,developed by George Dantzig in 1946. It provides us with a systematic way of examiningthe vertices of the feasible region to determine the optimal value of the objective introduce this method with an we want to find the maximum value of where and subject to the following the left-hand side of each inequalityis less than or equal to the right-hand side, theremust exist nonnegative numbers and that can be added to the left side of each equa-tion to produce the following system of linear
The simplex method is carried out by performing elementary row operations on a matrix that we call the simplex tableau.This tableau consists of the augmented matrix corre-sponding to the constraint equations together with the coefficients of the objective function written in the form In the tableau, it is customary to omit the coefficient of z.
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