Consider the following optimization problem (P1). maximize 4x1 + 6x2 + 5x3+4x4 + 6x5 + 4x6 + 15x7 + 15x8 subject to 3x1 + 10x2 + 7x7 + 8x8 17, 5x1 + 2x2 + 4x7 + 3x8 7, 6x3 +9x4+x7 +10x8 13, 3x3 + 2x4 + 8x7 + 4x8 8, x5 + 4x6 + 2x7+7x8 8, 5x5 + 6x6 + 3x7 + 4x8 13, X1, X2, X3, X4, X5, X6, X7, X8 {0, 1}. (P) )Apply Lagrangian decomposition to (P1). Write down the re- formulated problem, show the relaxed constraints in the reformulated problem. Apply 2 iterations by hand-writing. Explicitly write down the master problem, subproblems, and each updating calculations, clearly. You may use subgradient algorithm or cutting planes algorithm, no need to use both. No need to apply Branch-and-Price, just solve the root node.