The Yasar Logistics soon will be hooking up computer terminals at each of its warehouses to the computer at its main office using special phone lines with telecommunications devices. The phone line from a warehouse need not be connected directly to the main office. It can be connected indirectly by being connected to another warehouse that is connected (directly or indirectly) to the main office. The only requirement is that every warehouse be connected by some route to the main office.

The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of warehouses is as follows:

Distance between Pairs of Warehouses (miles)

Main Office Warehouse 1 Warehouse 2 Warehouse 3 Warehouse 4

Main W.1 W.2

- 70 85 70 - 50 85 50 -

100 120 145 110 180 105

W.3 W.4

100 110 120 180 145 105

- 150 150 -

Management wishes to determine which pairs of warehouses should be directly connected by special phone lines in order to connect every warehouse (directly or indirectly) to the main office at a minimum total cost.

a. Solve the minimum spanning tree problem. Show the optimal solution on the network. (14 Points)

b. Determine the total length of the links. (3 Points) c. Determine the total cost in order to connect every warehouse to the main office. (3 Points)

3. The Yaar Logistics soon will be hooking up computer terminals at each of its warehouses to the computer at its main office using special phone lines with telecommunications devices. The phone line from a warehouse need not be connected directly to the main office. It can be connected indirectly by being connected to another warehouse that is connected (directly or indirectly) to the main office. The only requirement is that every warehouse be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of warehouses is as follows: Main Office Warehouse 1 Warehouse 2 Warehouse 3 Warehouse 4 Distance between Pairs of Warehouses (miles) Main W.1 W.2 W.3 W.4 70 85 100 110 70 - 50 120 180 85 50 145 105 100 120 145 150 110 180 105 150 Management wishes to determine which pairs of warehouses should be directly connected by special phone lines in order to connect every warehouse (directly or indirectly) to the main office at a minimum total cost. a. Solve the minimum spanning tree problem. Show the optimal solution on the network. (14 Points) MO W3 wi W2 W4 b. Determine the total length of the links. (3 Points) c. Determine the total cost in order to connect every warehouse to the main office. (3 Points) 3