Final answer:
The balance of flow rule that applies when Total Supply < Total Demand in a network problem is the Conservation of demand. This ensures that network flows fulfill demand as far as the limited supply allows.
Step-by-step explanation:
When Total Supply is less than Total Demand in a network problem, the balance of flow rule that applies is c) Conservation of demand. This means that the network flows must be managed in such a way that the total demand is satisfied to the extent that the limited supply permits. In a practical sense, the insufficient supply must be allocated across the network to meet as much of the demand as possible, while ensuring that no more is supplied than is available. This is an application of linear programming in operations research, particularly in transportation and allocation problems where supply and demand constraints play a crucial role.