For a minimum-cost flow problem to have a feasible solution, which of the following mustbe true?A) There is the same number of supply nodes and demand nodes.B) There is only one supply node and one demand node.C) There is an equal amount of supply and demand.D) The supply and demand must be integers.E) The transshipment nodes must be able to absorb flow.
Question
For a minimum-cost flow problem to have a feasible solution, which of the following mustbe true?A) There is the same number of supply nodes and demand nodes.B) There is only one supply node and one demand node.C) There is an equal amount of supply and demand.D) The supply and demand must be integers.E) The transshipment nodes must be able to absorb flow.
Solution
The correct answer is C) There is an equal amount of supply and demand.
For a minimum-cost flow problem to have a feasible solution, the total supply must equal the total demand. This is because every unit of supply must have a corresponding unit of demand to flow towards. If there is more supply than demand, there would be excess supply with nowhere to go. Conversely, if there is more demand than supply, there would be demand that cannot be satisfied. Therefore, the total supply must equal the total demand for a feasible solution to exist.
The other options are not necessarily true. For example, there doesn't need to be the same number of supply nodes and demand nodes (A), there doesn't need to be only one supply node and one demand node (B), the supply and demand don't have to be integers (D), and the transshipment nodes don't necessarily need to be able to absorb flow (E).
Similar Questions
Which of the following is not an assumption of a minimum-cost flow problem?A) At least one of the nodes is a supply node.B) There is an equal number of supply and demand nodes.C) Flow through an arc is only allowed in the direction indicated by the arrowhead.D) The cost of the flow through each arc is proportional to the amount of that flow.E) The objective is either to minimize the total cost or to maximize the total profit.
Which of the following will have negative net flow in a minimum-cost flow problem?A) Supply nodesB) Transshipment nodesC) Demand nodesD) Arc capacitiesE) None of the choices is correct.
A minimum-cost flow problem is a special type of:A) linear programming problem.B) transportation problem.C) spanning tree problem.D) transshipment problem.E) maximum flow problem.
The unbalanced transportation problem where the total supply exceeds total demand is the case where: In a transportation problem with three locations and two destinations, the objective function is as follows: Min 20X11 + 18X21 + 23 X31 + 16X12 + 14X22 + 12X32. How much does it cost to ship one unit from location 2 to destination 1?
When the total demand is equal to supply, then the transportation problem is said to be ______________a.balancedb.unbalancedc.maximisationd.minimisation
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