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Consider the following Linear Programming Problem

Min $z=2x_1 + 3x_2 + x_3$

Sub to $x_1 + 2x_2 + 2x_3 - x_4 +x_5=3$

$2x_1 + 3x_2 + 4x_3 + x_6=6$

$x_i\geq 0$, $i=1,......., 6$

A non-degenerate basic feasible solution $(x_1, x_2, x_3, x_4, x_5, x_6)$ is

1) (1, 0, 1, 0, 0, 0)

2) (1, 0, 0, 0, 0, 7)

3) (0, 0, 0, 0, 3, 6)

4) (3, 0, 0, 0, 0, 0)

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  • $\begingroup$ please help..... $\endgroup$ – 1256 Jan 10 '18 at 13:25
  • $\begingroup$ What do you know about the rank of the constraint matrix? Can you recall the definition of BFS? HInt: (2) is not even a FS. (4) has too many zeros. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Jan 11 '18 at 16:59
  • $\begingroup$ It might help to have a look at this closely related question. $\endgroup$ – Axel Kemper Jan 12 '18 at 10:12
  • $\begingroup$ yes, got it..... $\endgroup$ – 1256 Jan 12 '18 at 10:24

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