Q1) Consider the following optimization problem (P1). maximizesubjectto4x1+6x2+5x3+4x4+6x5+4x6+15x7+15x83x1+10x2+7x7+8x8175x1+2x2+4x7+3x876x3+9x4+x7+10x8133x3+2x4+8x7+4x88x5+4x6+2x7+7x885x5+6x6+3x7+4x813x1,x2,x3,x4,x5,x6,x7,x8{0,1}. a.) (25 pts) Apply Lagrangian decomposition to (P1). Write down the reformulated 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