268 Consider the following minimum-cost flow model: (8) Network Models (5, $6.1) (8) (7,$5) (4, $4.4)...

  

Transcribed Image Text:

268 Consider the following minimum-cost flow model: (8) Network Models (5, $6.1) (8) (7,$5) (4, $4.4) (4, $2) A (6, $5.5) (3, $7) (5, $5) We wish to send eight units from node 1 to node 5 at minimum cost. The numbers next to the arcs indicate upper bounds for the flow on an arc and the cost per unit of flow. The following solution has been proposed, where the numbers next to the arcs are flows. (5, $3) 3 (4, $3.2) (-8) (-8) The total cost of the proposed solution is $66.8. a) Is the proposed solution a feasible solution? Is it a basic feasible solution? Why? b) How can the proposed solution be modified to constitute a basic feasible solution? c) Determine multipliers on the nodes associated with the basic feasible solution given in (b). Are these multipliers unique? d) Show that the basic feasible solution determine in (b) is not optimal. e) What is the next basis suggested by the reduced costs? What are the values of the new basic variables? Nonbasic variables? 268 Consider the following minimum-cost flow model: (8) Network Models (5, $6.1) (8) (7,$5) (4, $4.4) (4, $2) A (6, $5.5) (3, $7) (5, $5) We wish to send eight units from node 1 to node 5 at minimum cost. The numbers next to the arcs indicate upper bounds for the flow on an arc and the cost per unit of flow. The following solution has been proposed, where the numbers next to the arcs are flows. (5, $3) 3 (4, $3.2) (-8) (-8) The total cost of the proposed solution is $66.8. a) Is the proposed solution a feasible solution? Is it a basic feasible solution? Why? b) How can the proposed solution be modified to constitute a basic feasible solution? c) Determine multipliers on the nodes associated with the basic feasible solution given in (b). Are these multipliers unique? d) Show that the basic feasible solution determine in (b) is not optimal. e) What is the next basis suggested by the reduced costs? What are the values of the new basic variables? Nonbasic variables?