Consider the backpack problem $($linear programming problem$)$:

max z $=23$x$1+17$x$2+30$x$3+14$x$4+9$x$5$

subject to

$6$x$1+5$x$2+10$x$3+7$x$4+5$x$5<=14$

xi in $\{0,1\}$ i $=1,2,3,4,5$

$($a$)$ Apply the Branch & Bound algorithm to solve it$.$ Ensure that the selection of the next node for branching is done each time based on the best value of the objective function $($Jumbtracking or Best First$).$

$($b$)$ For the above problem, is it possible to tighten the basic constraint of the problem to facilitate the algorithmic process of finding the best value?

$($c$)$ Using the constraint of the above problem propose cutoff levels from three different minimum coverages of the problem. $($Note: There are more than three$).$ How is the tree of Branch & Bound formed after the introduction of cutoff levels?

Please adress each question individually!