Simplex method in prime how to use the constrains maximise s.t. constraints.

[Albert Chan]

(11-05-2023 11:05 PM)Anthony The Koala Wrote:  I appreciate please an elaboration of:
(i) it needs to satisy all constraints, and
(ii) most of them not vertices. What are these vertices

(i) Of course solution need to satisfy all constraints (it is given!)

Intersection of 2 constraints only implied these 2 are satisfied.
The point may satisfied other constraints, but it is not guaranteed.

(ii) HPCarnace post #5 have a nice picture.
https://www.hpmuseum.org/forum/attachment.php?aid=12759

Purple regions are feasible solution, satisfied all constraints.
When I say vertices, I am referring to the vertices of this purple polygon.

To minimize cost, solution must be on the edge of feasible region.
If cost function slope is different than constraints, solution is on one of the vertices.

There are line intersecting points outside purple region, those are not vertices.
Getting those points are just a waste of time, even if cost is lower.