Q$1.$ Suppose we have obtained the tableau below for a maximization problem. State conditions on

$a_1,a_2,a_3,b,c_1,$ and $c_2$ that make the following statements true: $(30$p$)$

a$)$ The current solution is optimal, and there are alternative optimal solutions.

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

c$)$ The current basic solution is a degenerate basic feasible solution.

d$)$ The current basic solution is feasible, but the LP is unbounded.

e$)$ The current basic solution is feasible, but the objective function value can be improved by

replacing $x_6$ as a basic variable with $x_1.$