Notation of a linear inequality system. x 1 ≤ 0 x 2 ≤ 0 x 3 ≤ 0is that right?But what can I get from line 1? Thanks deeply for your help. min { 2 x 1 + 4 x 2 + 7 x 3 : 2 x 1 + x 2 + 6 x 3 ≥ 5 4 x 1 − 6 x 2 + 5 x 3 ≥ 8 x 1 , x 2 , x 3 ≥ 0 }

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Notation of a linear inequality system.      x      1    ≤  0      x      2    ≤  0      x      3    ≤  0is that right?But what can I get from line 1? Thanks deeply for your help.  min      {                            2                      x            1                    +          4                      x            2                    +          7                      x            3                    :                                      2                      x            1                    +                      x            2                    +          6                      x            3                    ≥          5                                      4                      x            1                    −          6                      x            2                    +          5                      x            3                    ≥          8                                                  x            1                    ,                                                                                        x            2                    ,                                                                             x            3                    ≥          0                      }

Kamora Greer · Accepted Answer

This notation doesn’t only describe a system of linear inequalities but a linear optimization problem. So line 1 is the objective function and the other lines are a system of linear inequalities that describe the feasible region.By the way, this description is a use of set builder notation (with cleverly sized braces): The problem is to find the minimum of the set   {     f  (  x  )  :  P  (  x  )     } where   f is the linear function given by   f  (  x  )  =  2      x    1    +  4      x    2    +  7      x    3   and   P is the predicate described by the other lines.Your interpretation of the last line is correct (provided you meant to write   ≥ instead of   ≤).

Notation of a linear inequality system. x 1 </msub> ≤ 0

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