<div id="comment:0"></div> #18815 introduced `Polyhedron.to_linear_program` -- but there's very little one can do with it. To - set an objective other than the default 0; - access an optimal solution vector after solving, one needs the MIP variable (`x` in the code of `to_linear_program`). Currently the only way to do anything is by using the MIP backend. I would propose to return `x` as a second return value, but this of course changes the interface. CC: @nathanncohen @vbraun @videlec @fchapoton @dimpase @jdemeyer Component: **geometry** Author: **Matthias Koeppe** Branch/Commit: **[`280ba21`](https://github.com/sagemath/sagetrac-mirror/commit/280ba21e94f1cf40631b8b49c9e898f4a4d052f1)** Reviewer: **Dima Pasechnik** _Issue created by migration from https://trac.sagemath.org/ticket/20301_