(Solution) - Develop the B B tree for each of the following problems -(2025 Original AI-Free Solution)

Paper Details

Develop the B&B tree for each of the following problems. For convenience, always select x1 as the branching variable at node O.
*(a) Maximize z = 3Xl + 2X2
subject to
2x1 + 5x2 ? 5 9
4xl + 2x2 ? 9
x1, x2 ? 0 and integer
(b) Maximize z = 2x1 + 3x2
subject to
5x1 + 7x2 ? 35
4xl + 9x2 ? 36
xl, x2 ? 0 and integer
(c) Maximize z = x1 + x2
subject to
2x1 + 5x2 ? 16
6xl + 5x2 ? 27
xl > x2 ? 0 and integer
*(d) Minimize z = 5x1 + 4x2
subject to
3x1 + 2x2 ? 5
2x1 + 3x2 ? 7
xl, x2 ? 0 and integer
(e) Maximize z = 5x1 + 7X2
subject to
2xl + x2 ? 13
5xi + 9x2 ? 41
xl > x2 ? 0 and integer