Consider the ILP max 30x1 + 55x2 + 20x3 s .t. 40x1 - 12x2 + 11x3 … 55 19x1 + 60x2 + 3x3 Ú 20 3x1 + 2x2 + 2x3 = 5 x1, x2, x3 = 0 or 1 Form the Lagrangian relaxations obtained by dualizing each of the following collections of main constraints, and show all sign restrictions that apply to Lagrange multipliers.

(a) Dualize that first and second main constraints.

(b) Dualize the first and third main constraints.