Consider the following algorithm for solving a linear program in standard form without having to use the Big-M method:
Choose any basis.
Check to see if this basis is primal feasible.
If so, use this as your initial BFS and solve the problem with simplex.
If the basis is primal infeasible, solve the problem using dual simplex
a) How would you find a basis to start this algorithm?
b) How would you check to see if this basis is primal feasible?
c) Do you think this algorithm will work? Why or why not?