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# GE330_lect4 - Lecture 4 Simplex Algorithm Path February 2...

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Lecture 4 Simplex Algorithm Path February 2, 2009

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Angelia Nedi´ c Lecture 4 Path of the Simplex Method Simplex method does not enumerate all the basic solutions It moves from a basic feasible to another (better) basic solution iteratively until it reaches an optimal solution The move to another basic solution with improved value is attained by changing only one basic variable at a time Operations Research 1
Angelia Nedi´ c Lecture 4 Operations Research 2

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Angelia Nedi´ c Lecture 4 Illustration of the Path A4- 0 *y= O Operations Research 3
Angelia Nedi´ c Lecture 4 Suppose we are maximizing z = 2 x 1 + 3 x 2 , and suppose we start at x 1 = 0 and x - 2 = 0 . I we change one variable at a time, the function increases by 2 for every unit increase in x 1 and by 3 for every unit increase in x 2 . Simplex will first choose to increase x 2 as much as possible (while staying feasible), and then it will increase x 2 The preceding defines a path from A to B to C , which is the simplex path .

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