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[4.7] Phase I of the two-phase method can be made use of to check redundancy. Suppose that we have the following three constraints:

X1 - 2x2 > 2

X1 + 3x2 > 4

2X1 + x2 > 6

Note that the third constraint can be obtained by adding the first two constraints. Would Phase I detect this kind of redundancy? If not, what kind of redundancy will it detect? Does the type of redundancy in which some inequality holds whenever the other inequalities hold imply degeneracy? Discuss.

Philp Chen
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1 Answers1

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You have 3 surplus variables so there will be 3 artificial variables needed. As you should know, for phase 1 your objective function is minimization of sum of artificial variables. You simply solve phase 1 and at the end of third iteration, two basic variables out of 3 become 0. The value of zero in right hand side column means a degeneracy had been occurred. Of course you detected a redundancy in your constraints but you can't conclude that the redundancy is happened due to the fact that the third constraint was sum of the other two. so the answer is no! you can't detect this kind of redundancy with two-phase method.

For simplex tableau details I am attaching my solution: 1st page and 2nd page of solution

Yalda Yazdanpanah
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