How can we use Fourier-Motzkin elimination on system of inequalities with positive coefficients preceding each variable x 1 to x 2 . Obviously, in this case we will only have an upper bound as a solution but how do we find it.For example: 5 x 1 + 3 x 2 ≤ 8 2 x 1 + 5 x 2 ≤ 15

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How can we use Fourier-Motzkin elimination on system of inequalities with positive coefficients preceding each variable       x    1   to       x    2  . Obviously, in this case we will only have an upper bound as a solution but how do we find it.For example:  5      x    1    +  3      x    2    ≤  8  2      x    1    +  5      x    2    ≤  15

Khloe Jackson · Accepted Answer

Rewrite your two inequalities as      x    1    ≤      8    5    −      3    5        x    2      and        x    1    ≤      15    2    −      5    2        x    2  Then      x    1    ≤  min  {      8    5    −      3    5        x    2    ,      15    2    −      5    2        x    2    }This corresponds to the region of         R    2   below the graph of the function      x    1    =  f  (      x    2    )  =      {                                                      8              5                                −                                    3              5                                            x            2                                                if                                 x            2                    ≤                                    59              19                                                                                      15              2                                −                                    5              2                                            x            2                                                if                                 x            2                    &amp;gt;                                    59              19

How can we use Fourier-Motzkin elimination on system of inequalities with positive coefficients prec

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