Form the linear programming relaxation of each of the following ILPs. (a) min 12x1 + 45x2 +

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Form the linear programming relaxation of each of the following ILPs.

(a) min 12x1 + 45x2 + 67x3 + 1x4 s.t. 4x1 + 2x2 - x4 … 10 6x1 + 19x3 Ú 5 x2, x3, x4 Ú 0 x1 = 0 or 1 x3 integer

(b) max 3x1 + 8x2 + 9x3 + 4x4 s.t. 2x1 + 2x2 + 2x3 + 3x4 … 20 29x1 + 14x2 + 78x3 + 20x4 … 100 x1, x2, x3 = 0 or 1 x4 Ú 0

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