Consider the following transshipment network for finding the shortest route from node 1 to node 7.A network diagram between seven parties, distributed across four columns, is shown. The left-most column contains node 1. The second column contains nodes 2, 3, and 4. The third column contains nodes 5 and 6. The right-most column contains node 7. Arrows are shown between various locations. The following list contains the numbers placed on the graph.1→2: 71→3: 91→4: 182⇆3: 32⇆5: 53⇆2: 33⇆5: 44→6: 35⇆2: 55⇆3: 45⇆6: 25→7: 66⇆5: 26→7: 37: no departing arrows(a)Formulate a linear programming model of the problem. (Express your answers using xij, where each xij is either 0 or 1 for the arc from node i to node j.)Min s.t.Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows Node 7 Flows For all xij = 0, 1.(b)Find the shortest route from node 1 to node 7 in the network shown. (Enter your answers as a comma-separated list.)path = 1, , 7

The question presents a diagram of a network with nodes and arrows representing the routes between…

Answered: Consider the following transshipment…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Consider the following transshipment network for finding the shortest route from node 1 to node 7.

A network diagram between seven parties, distributed across four columns, is shown. The left-most column contains node 1. The second column contains nodes 2, 3, and 4. The third column contains nodes 5 and 6. The right-most column contains node 7. Arrows are shown between various locations. The following list contains the numbers placed on the graph.

1→2: 7
1→3: 9
1→4: 18

2⇆3: 3
2⇆5: 5

3⇆2: 3
3⇆5: 4

4→6: 3

5⇆2: 5
5⇆3: 4
5⇆6: 2
5→7: 6

6⇆5: 2
6→7: 3

7: no departing arrows

(a)

Formulate a linear programming model of the problem. (Express your answers using x_ij, where each x_ij is either 0 or 1 for the arc from node i to node j.)

Min

s.t.Node 1 Flows

Node 2 Flows

Node 3 Flows

Node 4 Flows

Node 5 Flows

Node 6 Flows

Node 7 Flows

For all x_ij = 0, 1.

(b)

Find the shortest route from node 1 to node 7 in the network shown. (Enter your answers as a comma-separated list.)

path = 1,

, 7

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