Determine the best bound on the optimal solution value of an ILP with each of the following objective functions that is available from the specified LP relaxation optima x .

(a) max 24x1 + 13x2 + 3x3 x 

= a2, 12

, 0b

(b) min x1 - 6x2 + 49x3 x 

= a1, 0, 27 b

(c) min 60x1 - 16x2 + 10x3 x 

= a12

, 1, 12 b

(d) max 90x1 + 11x2 + 30x3 x 

= a0, 12

, 3b