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.

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.

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.

Which of the following is not an assumption of a shortest path problem?A) The lines connecting certain pairs of nodes always allow travel in either direction.B) Associated with each link or arc is a nonnegative number called its length.C) A path through the network must be chosen going from the origin to the destination.D) The objective is to find a shortest path from the origin to the destination.E) None of the choices is correct

The diagram below shows an input network for the minimum-cost flow problem, and the flow (shown in red) in this network at the end of the 2-nd iteration of the Successive Shortest Path algorithm. During the computation, whenever there is a choice of a vertex, the algorithm selects the vertex which is first in the lexicographical order. (This means, for example, that during the first iteration, the algorithm selected vertex p1 from the two available supply vertices, and selected vertex r1 from the two available demand vertices.) Complete the following statements by dragging and dropping appropriate options.There was  Blank 1 Question 1 path from p2 to r1 in the residual network at the beginning of the 2-nd iteration.At the end of the 2-nd iteration, the flow saturates  Blank 2 Question 1 edges.At the beginning of the 3-rd iteration, the residual supply at vertex p2 is  Blank 3 Question 1 .In the residual network constructed in the 3-rd iteration,  Blank 4 Question 1 vertices are reachable from vertex p2.The cost of the path selected in the residual network in the 3-rd iteration is  Blank 5 Question 1 .The flow in the input network computed by the end of the 3-rd iteration  Blank 6 Question 1 satisfy all supply and demand.