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## Re: [Help-glpk] Understanding solution answer: infeas??

**From**: |
Andrew Makhorin |

**Subject**: |
Re: [Help-glpk] Understanding solution answer: infeas?? |

**Date**: |
Mon, 2 Nov 2009 21:16:59 +0300 |

>* Hi guys, I am new in GLPK use and I would like to ask you about some*
>* solution that I get: Basically I define an LP problem where the*
>* variable x10, x11 and x12 take values bw. 0 and 1 and the sum of*
>* x10+x11+x12 = 1, according to that and for 18 structural variables I*
>* get the following answer:*
>* ./a.out*
>* 0: obj = 0.000000000e+00 infeas = 6.000e+00 (0)*
>* * 8: obj = 1.300000000e+03 infeas = 0.000e+00 (0)*
>* * 13: obj = 1.600000000e+03 infeas = 8.171e-16 (0)*
>* OPTIMAL SOLUTION FOUND*
>* z = 1600*
>* x10 = 0; x11 = 0; x12 = 1*
>* x20 = 0; x21 = 0; x22 = 1*
>* x30 = 0; x31 = 0; x32 = 1*
>* x40 = 0; x41 = 0; x42 = 1*
>* x50 = 1; x51 = 0; x52 = -8.17124e-16*
>* x60 = 1; x61 = 0; x62 = 0*
>* The value of z correspond to the right value, but how do I understand*
>* the value of x52??, is it a real "0" value and how is it related to*
>* the "infeas = 8.171e-16" value?, does it mean that my answer is wrong*
>* (since I should have only expect x50 = 1; x51 = 0; x52 = 0)?*
The solution is correct. You should understand x52 = -8.17124e-16 as
zero within a working precision. To perform calculations the glpk
simplex solver uses floating-point arithmetic, so it reports a solution,
which is an approximation to the mathematically exact result.