Question

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.

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.

Answer 1

The origin is node 1. The transshipment nodes are 2, 3, 4, 5, and 6. The destination is node 7.

A linear program model is a mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables. Let represent the arc from node to node.

Use EXCEL to solve for the optimal solution report using the following steps.

1. Select Solver from the Analysis Group in the Data Ribbon

2. Enter the proper values for the constraints and the objective function

3. Select Simplex LP

4. Click the checkbox for Make Unconstrained Variables Non-negative

5. Click Solve

The maximum value for is 10. In other words, the maximum flow is 10,000 messages.

Answer 2

The origin is node 1. The transshipment nodes are 2, 3, 4, 5, and 6. The destination is node 7

Answer 3

The origin is node 1. The transshipment nodes are 2, 3, 4, 5, and 6. The destination is node 7

Answer 4

1.      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.

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.

Answer 5

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