We investigate the combinatorial structure of linear programs on
simple $d$-polytopes with $d+2$ facets. These can be encoded by {\em
admissible} grid orientations. Admissible grid orientations are also
obtained through orientation properties of a planar point
configuration or by the dual line arrangement. The point configuration and the
polytope corresponding to the same grid are related through an
extended Gale transform.
The class of admissible grid orientations is shown to contain
non-realizable examples, i.e., there are admissible grid orientations which
cannot be obtained from a polytope or a point configuration.
It is shown, however, that every admissible grid orientation
is induced by an arrangement of pseudolines.
This later result is used to prove several nontrivial
facts about admissible grid orientations.