Need to find a solution to the following system of linear inequalities: <mtable columnalign="ri

Nicholas Cruz

Nicholas Cruz

Answered question

2022-05-22

Need to find a solution to the following system of linear inequalities:
x 1 x 2 1 x 1 x 4 4 x 2 x 3 2 x 2 x 5 7 x 2 x 6 5 x 3 x 6 10 x 4 x 2 2 x 5 x 1 1 x 5 x 4 3 x 6 x 3 8
Is there any systematic way to find a solution?

Answer & Explanation

hoffwnbu

hoffwnbu

Beginner2022-05-23Added 13 answers

Using linear programming (LP) with a constant zero objective, I found the following feasible solution:
x = ( 6 , 0 , 2 , 8 , 7 , 0 ) .
By the way, this LP is the dual of a network LP, hence the constraint matrix is totally unimodular.

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