Branch-and-bound reacts to a fractional LP optimum by splitting the problem. The split is exact: one child takes the floor side and the other takes the ceiling side. This lesson shows the first branch of the IP-B search.
highlighted = computed this step
Fractional coordinate
At the root, the LP relaxation gives (3, 1/2) with bound 10. Why: the fractional y value prevents this point from being an integer solution.
zLP=10
Split without losing integers
The branch is y at most 0 or y at least 1. Why: every integer y value is on exactly one side of that split.
y≤0ory≥1
Diagram note
The tree prefix is recomputed from the full branch-and-bound search, then clipped to the first branch. Pixel positions are rounded for layout; every number shown is exact.