How to get multiple BFS using lpsolve

Question

I'm trying to use lpsolve IDE to solve LPs with multiple BFS, however only one solution is generated. What should I do?

min 2x1 + 4x2 + 7x3
st 2x1 + x2 + 6x3 >= 5
4x1 - 6x2 + 5x3 >= 8
x1 >= 0
x2 >= 0

I only get x1 = 2.5, x2 = x3 = 0 But there are other BFS eg (0,0,8.5), (19/8,1/4,0)

Answer 1

LP solvers typically just return one solution. With some solvers, you may be able to find out what solutions were visited (I am not sure that can be done with lpsolve).

Enumerating all BFS is not that easy. Here is a (somewhat complicated) way to enumerate optimal solutions. This can also be used to enumerate all (or many) feasible solutions.