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# HW4 - in row 0 d Insert the current basic feasible solution...

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4. Homework for IEOR162 Linear Programming Semester: Fall 2010 Instructor: Dr. Sarah Drewes Due to: Tue, October 19, 2010 (at the beginning of class) P1 Consider the following LP: max z = 3 x 1 + x 2 s.t. 2 x 1 + x 2 6 x 1 + 3 x 2 9 x 1 , x 2 0 a) Solve the given LP using the simplex algorithm. b) Graph the two-dimensional feasible region and the basic feasible solutions that are visited during the algorithm. c) Peform now again the first iteration of the simplex algorithm for this problem, where you choose not the variable with the most negative coefficient in row 0 as entering variable, but the variable with the negative coefficient that has the smallest absolute value

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Unformatted text preview: in row 0. d) Insert the current basic feasible solution after this iteration into the graph. What basic feasible solutions will be visited by the simplex algorithm starting from this current bfs? Why? P2 We just take the variable with the most negative coeﬃcient in row 0 as entering variable. It can be suggested that at each iteration of the 1 simplex algorithm, the entering variable should be the variable that would bring the greatest increase in the objective function. Why is this rule hardly ever used although it usually results in fewer iterations? 2...
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