Consider the given simplex tableau corresponding to a basic solution of a maximization LP$.$z x$1$ x$2$ x$3$ x$4$ x$5$ x$6$ RHS z $1200$ a $0$ b $13$ x$30-201-40$ c $5$x$20$ d $10$ e $0-2$ fx$5020031-411.$ 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