I'm supposed to find the basic solutions of the given LPP graphically. I know what a bfs means, I can find that in other way (I mean by method mentioned in this post), but I don't know how to do it graphically. The system is:- $$2x + 3y \leq 21$$$$ 3x - y \leq 15$$$$ x + y \geq 5$$$$ y \leq 5$$ $$ x, y \geq 0$$ Any hint/solution would be appreciated. Thanks!

  • $\begingroup$ Since you only have two variables you can plot each inequality in the plane and take the intersection, maybe this is what they mean by graphically? $\endgroup$ – TSF Feb 3 '19 at 13:12
  • $\begingroup$ @TonyS.F. but that'll be a feasible solution. Not bfs if I'm not wrong... $\endgroup$ – Ankit Kumar Feb 3 '19 at 13:13
  • $\begingroup$ It depends on which one you pick, of course. You will get a polygon of sorts in the plane and if you pick a vertex you will have BFS. $\endgroup$ – TSF Feb 3 '19 at 13:14

For a linear program like this, the set of all feasible solutions is the intersection of half spaces and thus a polyhedron. A BFS corresponds to a vertex of this polyhedron.

Now, since we only have 2 variables we can plot all our half spaces in the plane and take the intersection to get a polygon. Then, the BFS are just the vertices of this polygon.

Here is a graph of your problem (more or less)

From that graph we can see (0,5), (5,0), (3,5), and (6,3) are all BFS.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.