Question $2$

Consider the given simplex tableau corresponding to a basic solution of a maximization LP$.$

For each of the following cases, specify the conditions on the parameters $($a$,$ b$,$ c$,$ d$,$ e and f$)$ that

make the statement true. For each case, assign a value to each unknown, and write the current bfs$.$

i$)$ The current basic solution is the unique optimal.

ii$)$ The current basic solution is not a basic feasible solution.

iii$)$ The current tableau shows that the LP is unbounded.

iv$)$ The current basic solution is feasible, but can be improved by $x_4$ entering, and $x_5$ leaving the

PRACTICE $3$

basis.

v$)$ The current basic solution is optimal, and there are alternate optimal solutions.

vi$)$ The current basic solution is feasible and degenerate but the pivot is not degenerate.

vii$)$ The current basic solution is feasible and the pivot is degenerate.

For case iii, provide the ray of unboundedness.

For case $v,$ provide the set of alternate optimal solutions.

For case vii, find the objective value and the bfs that corresponds to the next tableau without

performing simplex iterations.