HW3_Solutions

# HW3_Solutions - ORIE 3300/5300 ASSIGNMENT 3 SOLUTION Fall...

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Unformatted text preview: ORIE 3300/5300 ASSIGNMENT 3 SOLUTION Fall 2008 Problem 2 Grading scheme: 6 points for simplex, 2 points for picture, 2 points for finding other solution.-1 if not finding alternate solution directly from the final tableau. please mention to follow directions about pivoting next time, (esp for upcoming hw) After introducing the slack variables, the initial tableau is as follows: z- 2 x 1- 3 x 2- x 3 = 0 x 1 + x 4 = 2 x 2 + x 5 = 2- x 1 + x 3 + x 6 = 2 x 1 + x 2 + x 7 = 3 . The current basic feasible solution is x = [0 , , , 2 , 2 , 2 , 3] T , and the corre- sponding point in the polyhedron is [ x 1 ,x 2 ,x 3 ] T = [0 , , 0] T . Using the least index rule, x 1 will enter the basis (its reduced cost is 2, the negative of its coefficient in the top row). x 4 will leave the basis according to the minimum ratio test (2 / 1 < 3 / 1, ratios 2 / 0 and 2 / (- 1) ignored). Thus the next tableau is: z- 3 x 2- x 3 + 2 x 4 = 4 x 1 + x 4 = 2 x 2 + x 5 = 2 x 3 + x 4 + x 6 = 4 x 2- x 4 + x 7 = 1 . The current basic feasible solution is [2 , , , , 2 , 4 , 1] T , and the correspond- ing point in the polyhedron is [2 , , 0] T . x 2 enters the basis, and x 7 leaves the basis. The next tableau is: z- x 3- x 4 + 3 x 7 = 7 x 1 + x 4 = 2 x 4 + x 5- x 7 = 1 x 3 + x 4 + x 6 = 4 x 2- x 4 + x 7 = 1 . 1 The current basic feasible solution is [2 , 1 , , , 1 , 4 , 0] T , and the correspond- ing point in the polyhedron is [2 , 1 , 0] T ....
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HW3_Solutions - ORIE 3300/5300 ASSIGNMENT 3 SOLUTION Fall...

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