The following mixed-integer linear programming problem P0 should be solved using the branch-and-bound method: maxs.t.z=2x1+x23x1+2x265x1+2x28x1,x20andinteger The solution of the relaxed problem P0, that omits the integer restrictions, is x1=1,x2=1.5 and z=3.5. a) What is the lower bound z at the start of the problem? b) What is the upper bound z0 of the problem P0 ? c) Suggest the introduction of two new constraints that further branch the problem P0 into two subproblems in a reasonable way, using x2. Along the further branching process, the sub-problems visualized in the graph have been evaluated. For each sub-problem, the values for x1,x2 and z are named for the corresponding relaxed problems. Assume that problems are evaluated from P1 to P6 in the given order. e) Referring to the graph, name the sub-problems that would be pruned. For each pruned sub-problem, state which of the cases named under d) applies. (For the home assignment: please refer to the numbering on slide 23 of lecture 06 , and assume problems are evaluated in the given order from 0 to 6.) f) What are the respective lower bounds for the overall problem after the evaluation of each sub-problem (from P0 to P6 )? g) Which solution would be returned as the optimal solution give the value of the objective function in the optimal solution.)