A simplex tableau corresponding to a linear program in maximization form is given below. Find a set of

values of the unknowns $a,b,c,d,e,f,g,h,i,j,k$ in each of the following cases.

$($a$)$ The tableau is optimal but the BFS is degenerate.

$($b$)$ The tableau is optimal and the optimal solution is unique.

$($c$)$ The tableau is optimal and there are at least two optimal basic feasible solutions.

$($d$)$ The tableau is optimal, there are alternative optimal solutions but no alternative optimal BFS$.$

$($e$)$ The underlying linear program is unbounded.