Solved

The Following ILP Is Being Solved by the Branch and Bound

question 44

Essay

The following ILP is being solved by the branch and bound method. You have been given the initial relaxed IP solution. Complete the entries for the 3 nodes and label the arcs when you branch on X2.
$\begin{array}{ll}\text { MAX: } & 50 \mathrm{X}_{1}+40 \mathrm{X}_{2} \\\text { Subject to: } & 2 \mathrm{X}_{1}+4 \mathrm{X}_{2} \leq 40 \\& 3 \mathrm{X}_{1}+2 \mathrm{X}_{2} \leq 30 \\& \mathrm{X}_{1}, \mathrm{X}_{2} \geq 0 \text { and integer }\end{array}$
Initial solution
X₁ = 5.0
X₂ = 7.5
Obj = 550
$The following ILP is being solved by the branch and bound method. You have been given the initial relaxed IP solution. Complete the entries for the 3 nodes and label the arcs when you branch on X2. \begin{array}{ll} \text { MAX: } & 50 \mathrm{X}_{1}+40 \mathrm{X}_{2} \\ \text { Subject to: } & 2 \mathrm{X}_{1}+4 \mathrm{X}_{2} \leq 40 \\ & 3 \mathrm{X}_{1}+2 \mathrm{X}_{2} \leq 30 \\ & \mathrm{X}_{1}, \mathrm{X}_{2} \geq 0 \text { and integer } \end{array} Initial solution X<sub>1</sub> = 5.0 X<sub>2</sub> = 7.5 Obj = 550$

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