Question: Q2) Consider the following optimization problem: maximize 3x1 + 8x2 + 9x3 + 4x4 + 12x5 + 11x6 subject to 8x1+15x2+13x3+19x4+20x5+14x6 62, x1 +20x2 +5x3

Q2) Consider the following optimization problem: maximize 3x1 + 8x2 + 9x3 + 4x4 + 12x5 + 11x6 subject to 8x1+15x2+13x3+19x4+20x5+14x6 62, x1 +20x2 +5x3 +15x4 +12x5 +4x6 36, 2x1 +3x2 +12x3 13, 5x2 +7x3 +13x4 14, 17x3 + 11x4 + 14x5 26, 12x4 + 19x5 + 7x6 22, x1,x2,x3,x4,x5,x6 {0,1}.

a.) Apply Lagrangian relaxation by relaxing the first constraint. Use both Cutting Plane Method and Subgradient optimization. Show master problem, subproblem, and each updating calculations, clearly. No need to hand-write all the iterations, three iterations are sufficient.

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