$3.$ You are given the following simplex tableau for a minimization problem:

x$1$ x$2$ x$3$ x$4$ x$5$

$10$ c $2000$

x$34$ a $2100$

x$4124010$

x$5$ b $13001$

State conditions on the unknowns a$1,$ a$2,$ a$3,$ b and c such that the following statements are

true

$($a$)$ The current solution is infeasible.

$($b$)$ The current solution is optimal.

$($c$)$ The current solution is degenerate.

$($d$)$ The current solution is optimal and there are multiple optimal solutions.

$($e$)$ The optimal value is unbounded.