# recn7 - in the ﬁnal tableau You will ﬁnd y satisfying A...

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ORIE 3300/5300 RECITATION 7 Wed October 20 – Tue October 26 Fall 2010 The recitation instructor will discuss the following problem from the ﬁrst prelim: max 3 x 2 - x 3 - x 2 + x 3 0 x 1 + 2 x 2 - x 3 4 - 5 x 1 + 2 x 2 + x 3 6 x 1 , x 2 , x 3 0 . After adding slack variables x 4 , x 5 , and x 6 , you reach a problem in standard equality form. Deﬁne c , A , and b from this standard equality form problem. The ﬁnal tableau for the problem is z + 5 4 x 5 + 1 4 x 6 = 13 2 2 x 1 + x 4 + 3 4 x 5 - 1 4 x 6 = 3 2 - x 1 + x 2 + 1 4 x 5 + 1 4 x 6 = 5 2 - 3 x 1 + x 3 - 1 2 x 5 + 1 2 x 6 = 1 . This corresponds to the basis B = [4 , 2 , 3]. The point now is to identify the basis matrix A B , ﬁnd its inverse A - 1 B , and from these generate all the entries
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Unformatted text preview: in the ﬁnal tableau. You will ﬁnd y satisfying A T B y = c B , the reduced costs c j-y T A j for each nonbasic index j , and the columns A-1 B A j for these indices in the body of the tableau. Do the exercise below with your declared partner (if you have one). Hand in your answer (and cover sheet) at the end of the Recitation. Work through as much as possible of Question 3-2 (on a transportation model) in the AMPL book. 1...
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