Question: Question 1 Given the following network with distances shown in miles, find the shortest route from node 1 to each of other nodes. 14 16

Question 1 Given the following network with distances shown in miles, find the shortest route from node 1 to each of other nodes. 14 16 10 30 18 12 30 40 26 Question 2 A long distance telephone company uses a fiber-optic network to transmit phone calls and other information between locations. Calls are carried through cable lines and switching nodes. A portion of the company's transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can be transmitted over that branch of the network. (a) To keep up with the volume of information transmitted between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city located at node 1 to a city located at node 7. (b) Considering the node 1 as origin and node 7 as destination, produce LP formulation of the flow network. 3 3 2

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