$(4)$ Suppose the following simplex table is obtained for a maximization problem.

z

State the conditions on $a_1,a_2,a_3,b,c_1,c_2$ that are required to make the following statement true;

$($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 bfs

$($d$)$ The current basic solution is feasible, but the L$.$P is us$,$bounded

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

by replactr: $x_i$ as a basic variable with $x_i.$