I’m solving a linear problem with JuMP and Gurobi, and for some formulations I end up getting the following behaviour:

```
Academic license - for non-commercial use only
Optimize a model with 6725 rows, 6346 columns and 17254 nonzeros
Coefficient statistics:
Matrix range [1e-07, 1e+07]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [4e-07, 1e+04]
Warning: Model contains large matrix coefficient range
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 3752 rows and 3944 columns
Presolve time: 0.01s
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 1.983774e+06 0.000000e+00 0s
Solved in 1501 iterations and 0.10 seconds
Infeasible model
```

For another slightly different formulation I get the following behaviour:

```
Academic license - for non-commercial use only
Optimize a model with 11717 rows, 28042 columns and 42022 nonzeros
Coefficient statistics:
Matrix range [1e-07, 1e+07]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [4e-07, 1e+04]
Warning: Model contains large matrix coefficient range
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...
Presolve removed 6345 rows and 17873 columns
Presolve time: 0.04s
Ordering time: 0.00s
Barrier statistics:
Dense cols : 5
AA' NZ : 3.203e+04
Factor NZ : 1.407e+05 (roughly 17 MBytes of memory)
Factor Ops : 1.899e+06 (less than 1 second per iteration)
Threads : 1
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 2.07059225e+11 0.00000000e+00 8.23e+04 0.00e+00 9.10e+07 0s
1 1.54480975e+11 -1.14052489e+19 6.12e+04 3.31e+02 4.76e+07 0s
2 1.51813177e+11 -7.80999362e+18 6.02e+04 1.78e+02 4.51e+07 0s
3 1.51787625e+11 1.02396826e+23 6.01e+04 6.55e+04 5.77e+17 0s
4 2.07059225e+11 0.00000000e+00 8.23e+04 0.00e+00 9.10e+07 0s
5 4.56873171e+11 1.32645209e+12 8.23e+04 5.01e+03 6.31e+08 0s
6 1.71300159e+13 3.64537610e+13 8.25e+04 8.04e+04 4.34e+10 0s
7* 6.13167144e+14 3.83194214e+15 1.46e+03 3.02e+03 9.62e+05 0s
8* 4.84800700e+14 4.41350337e+15 5.97e+00 4.29e+02 6.86e+02 0s
9* 4.85688050e+14 6.48184468e+18 2.27e-02 4.86e+03 1.72e+01 0s
10* 5.41950241e+14 2.31123405e+20 3.59e-04 8.06e+04 1.03e+00 0s
11* 3.65150700e+15 5.81597939e+21 6.48e-06 2.87e+04 3.23e-02 0s
12* 7.39521619e+17 1.91153773e+24 2.78e-08 2.87e+04 3.47e-04 0s
13* 2.00856258e+20 6.97456139e+27 1.16e-10 1.79e+06 4.30e-05 0s
14* 5.70132227e+20 7.42676517e+27 5.80e-11 1.16e+07 1.72e-05 0s
15* 5.67160405e+21 1.34732737e+28 8.55e-11 9.81e+05 1.81e-06 0s
16* 7.16629699e+22 8.91224219e+28 5.04e-11 1.16e+06 1.50e-07 0s
17* 1.43364707e+23 2.00534601e+29 5.04e-11 3.15e+06 8.12e-08 0s
18* 6.70396621e+24 9.25905832e+30 5.04e-11 1.53e+06 1.93e-09 0s
19* 6.62645808e+25 8.94264368e+31 5.04e-11 1.56e+06 2.16e-10 0s
20* 2.51510982e+27 3.23937260e+33 7.13e-11 1.21e+06 6.05e-12 0s
21* 4.75050996e+28 6.05403813e+34 4.25e-19 4.60e+06 3.41e-13 0s
22* 5.14534672e+29 6.14728408e+35 3.93e-20 4.03e+06 3.24e-14 1s
23* 9.04011922e+30 1.08644506e+37 7.13e-11 1.51e+06 2.04e-15 1s
24* 4.85776882e+31 6.79262814e+37 5.04e-11 2.51e+06 4.29e-16 1s
25* 2.00748030e+32 2.53176143e+38 5.04e-11 1.80e+06 1.17e-16 1s
26* 5.75209253e+32 6.73021608e+38 3.51e-23 2.14e+06 4.51e-17 1s
27* 1.14373815e+33 1.22404304e+39 1.77e-23 9.35e+05 2.16e-17 1s
28* 2.27956404e+33 2.08548685e+39 8.87e-24 7.34e+05 9.17e-18 1s
29* 1.97980222e+34 2.71902152e+40 1.02e-24 2.68e+06 1.09e-18 1s
30* 5.28152333e+34 7.63361159e+40 3.83e-25 4.37e+06 4.39e-19 1s
31* 6.80137849e+35 1.07539142e+42 2.97e-26 2.41e+06 3.83e-20 1s
Barrier performed 31 iterations in 0.70 seconds
Numerical trouble encountered
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 1.983774e+06 0.000000e+00 1s
Solved with dual simplex
Solved in 7608 iterations and 1.61 seconds
Infeasible model
```

What I don’t understand is why the solver declares the model to be infeasible AFTER iterating - surely for a linear problem this could / should be determined before solving? Is it possible that this is due to the large range of matrix coefficients?