Solve error with small LP

[jajhall]

The LP 2300.mps causes an immediate solve error in the simplex solve, claiming "unbounded in dual phase 1"

[jajhall]

Odd problem. Origin is primal feasible with one dual infeasibility of 0.000263582, so its square is less than the dual feasibility tolerance of 1e-7. Hence HEkkDual::solve forces phase2 with the argument that the small dual infeasibility will be shifted. However, since the basis is primal feasible, no dual phase 2 iterations will be performed, so simplex reverts to Phase 1, and identifies dual-phase-1-unbounded. This is not possible, since the objective is bounded by 0, so HighsModelStatus::kSolveError is set.

If forcing phase 2 is prevented, dual phase 1 runs fine (3 iterations required) and then phase 2 completes correctly.

So, why is the first iteration of dual phase 1 different when no dual phase 2 iterations are performed?