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Unformatted text preview: OR3300/5300 Fall 2011 Prof. Bland Whose tableau is it anyway? Lets take a quick look at the simplex method as applied to Grandmas l.p. problem. Following the notation of section 5 of your notes the initial tableau or dictionary is the following system of linear equations. 1 z 20 x 1 30 x 2 = 2 x 1 + 2 x 2 + 1 x 3 = 80 4 x 1 + 2 x 2 +1 x 4 = 120 3 x 1 + 6 x 2 + 1 x 5 = 210 If we select x 1 to enter the basis, then x 4 must leave, and the second tableau or dictionary is the system of equations: 1 z 20 x 2 + 5 x 4 = 600 1 x 2 + 1 x 3 1 2 x 4 = 20 1 x 1 + 1 2 x 2 + 1 4 x 4 = 30 9 2 x 2 3 4 x 4 + 1 x 5 = 120 In a moment we will carry out more simplex pivots until we reach an optimal solution. Before we do that, lets simplify the notation a little, in conformity with the conventions in most linear programming books. In each row we will write down the coefficients of the variables without repeating the variable names (linear lagebra texts refer to this presentation of a system of linear...
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