Develop the B&B tree for each of the following problems. For convenience, always select x1 as the branching variable at node 0.

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(a) Maximize z = 3x1 + 2x2 subject to 2x1 + 5x2 … 18 4x1 + 2x2 … 18 x1, x2 Ú 0 and integer

(b) Maximize z = 2x1 + 3x2 subject to 7x1 + 5x2 … 36 4x1 + 9x2 … 35 x1, x2 Ú 0 and integer

(c) Maximize z = 2x1 + 2x2 subject to 2x1 + 5x2 … 27 6x1 + 5x2 … 16 x1, x2 Ú 0 and integer

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(d) Minimize z = 5x1 + 4x2 subject to 3x1 + 2x2 Ú 5 2x1 + 3x2 Ú 7 x1, x2 Ú 0 and integer

(e) Maximize z = 5x1 + 7x2 subject to 2x1 + x2 … 13 5x1 + 9x2 … 41 x1, x2 Ú 0 and integer