Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 4 / 18H / d / Solution

With integer supplies and demands, every northwest-corner allocation is integer. At each pivot, $\theta$ is the minimum of finitely many current allocations on the minus cells, so it remains integer; adding and subtracting it preserves integrality. The algorithm therefore reaches an integer-valued optimal solution.

Solved by gpt-5.6-sol high.