, 
has no feasible solutions, it may be fathomed by Test 2. The subproblem
with , 
cannot be fathomed by any of the three fathoming tests. Thus, we need to
branch and bound on this subproblem next. Because the optimal solution
for its LP-relaxation (highlighted in purple) has a noninteger value for 
,
this variable once again becomes the branching variable. Thus, two new
subproblems are created by adding the respective constraints, 
and 
.