Question

In a minimum-cost flow problem, which of the following is TRUE?

1) A feasible solution will exist if and only if total supply matches total demand
2) The number of supply nodes can be different from the number of demand nodes
3) There is at least one supply node

Answer 1

In a minimum-cost flow problem, a feasible solution will exist if total supply matches total demand, the number of supply nodes can differ from the number of demand nodes, and there is always at least one supply node.

Step-by-step explanation:

In a minimum-cost flow problem:

1. A feasible solution will exist if and only if the total supply matches total demand. This means that the amount of goods available is equal to the amount of goods needed.
2. The number of supply nodes can be different from the number of demand nodes. This means that there can be more or fewer sources of supply compared to the number of destinations or demands.
3. There is always at least one supply node. There must be at least one source of supply for the flow problem to have a solution.