Question

The preliminary layout of communications network has been determined and isillustrated in the accompanying network diagram.The links of this network aredepicted as branches,or arcs between each node,and the cost of transmitting

asingle message unit is indicated in parentheses beside each link.The nodes of thenetwork(with the exception of nodes 1 and 5,which are simply transmission andreception terminals)actually represent repeater stations (whose purpose is toreceive,amplify,error-check,and transmit any messages incident to the node),whose cost is a linear function of the (maximum)number of messages received,per second,at the station.Further,there are limits to the message units per secondthat may be transmitted via each link.We wish to determine the minimal-costdesign of this network if the maximum (i.e.,worst case)message load betweenterminals(nodes)1 and 5 is to be 500,000 messages per second.The accompanyingnetwork diagram and tables provide a summary of the data to be used in con-structing a model for this problem.Formulate the baseline model forthisproblem.($4)2(53)($3)85(56)(57)3

Fig: 1