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MIE376 Lec 3 - Revised Simplex.page3

MIE376 Lec 3 - Revised Simplex.page3 - MIE376 Mathematical...

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MIE376 Mathematical Programming Lecture Notes Daniel Frances © 2011 3 ( ) ( ) ( ) 2 1 2 1 1 1 3 1 1 0 0 1 0 0 1 = = T N T B c N B c and x2 is the entering variable Departing Variable Recall the original constraints Bx B + Nx N = b Recall that in the substitution method we were expressing the basic variables in terms of the non-basic variables This can be done simply using the matrix notation as we did before x B =B -1 b- B -1 Nx N . or using our example in the first iteration 2 1 2 1 4 3 1 3 1 1 7 16 1 1 3 1 7 16 x x x x x x = = As with the substitution method, as x 2 grows many basic variables may decrease. The departing variable is the basic variable that reaches zero first. Clearly we need to compare 16/3 and 7/1; the smallest ratio – with a
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