A transportation plan is feasible when every source ships its supply and every demand point receives its demand. The displayed plan is recomputed before it is painted.

highlighted = computed this step

Shipment Matrix

The recomputed shipment sends 2 from A to X, 1 from A to Y, 0 from B to X, and 2 from B to Y. Motivation: a plan is a full matrix, not just one attractive arc choice.

xAX=2xAY=1xBX=0xBY=2x_{AX}=2\quad x_{AY}=1\quad x_{BX}=0\quad x_{BY}=2
optimal transportation plan, cost 11XYsupplyA213B022demand235total cost11

Conservation

A ships 3, B ships 2, X receives 2, and Y receives 3. Interpretation: feasibility is exactly row sums meeting supply and column sums meeting demand.

row sums and column sums match the pinned totals\text{row sums and column sums match the pinned totals}
optimal transportation plan, cost 11XYsupplyA213B022demand235total cost11

Diagram note

Certificate note: the table shows a feasible balanced shipment and its recomputed total cost row. Pixel positions are rounded for layout; every number shown is exact.

feasibility is exact conservation\text{feasibility is exact conservation}
optimal transportation plan, cost 11XYsupplyA213B022demand235total cost11