Suppose that a minimizing ILP is being solved by LP-based branch and bound Algorithm 12A over decision variables x1, x2, x3 = 0 or 1, x4 Ú 0. Show how the search should process the node with x2 = 1 and other variables free if the corresponding LP relaxation has each of the following outcomes. Assume that the incumbent solution value is 100.

(a) x  = 10.9, 1, 0, 62, value n  = 97

(b) x  = 10.2, 1, 0.77, 4.52, value n  = 102

(c) x  = 11, 1, 0, 4.22, value n  = 75

(d) LP relaxation infeasible

(e) x  = 11, 1, 0.6, 02, value n  = 100

(f) x  = 10.4, 1, 0.1, 5.92, value n  = 86