Suppose that you are using the branch and bound (B & method to solve an integer

Question

Suppose that you are using the branch and bound (B & method to solve an integer program that has a minimization objective. Your B & B tree currently has six active nodes (a - f, below). The best feasible integer solution you have found so far has an objective value of 46. Clearly indicate which of the three actions (i - iii) you should take for each of the active nodes, given your current best solution. i. Branch on the node ii. Prune the node iii. Update your list of integer solutions with this solution and then prune the node (a) Feasible fractional solution with an objective value of 48 i ii iii (b) Feasible fractional solution with an objective value of 46 i ii iii (c) Feasible fractional solution with an objective value of 44 i ii iii (d) Infeasible fractional solution with an objective value of 45 i ii iii (e) Feasible integer solution with an objective value of 47 i ii iii (f) Feasible integer solution with an objective value of 45 i ii iii

Explanation / Answer

(a) PRUNE (ii)

(b) UPDATE (iii)

(c)BRANCH (i)

(d) PRUNE (ii)

(e)PRUNE (ii)

(f) BRANCH (i)

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