consider:

maximize x$1+$x$2,$

subject to x$1+$x$2>=2,$

$-$x$1+$x$2<=2,$

x$1,$x$2>=0,$

a$)$plot the feasible region. b$)$identify all the basic solutions and specify which are feasible and which are infeasible. c$)$solve the lp by the simplex algorithm and show that the algorithm stops