How do I do number 31? What do the numbers mean?

29 Coogan Construction is in the process of installing power lines to a large housing development. Rob Coogan wants to minimize the total length of wire used, which will minimize his costs. The housing development is shown as a network in Figure 19. Each house has been numbered, and the distance be- tween houses is given in hundreds of feet. What do you recommend? 30 The city of Six Mile, South Carolina, is considering making several of its streets one way. What is the maximum number of cars per hour that can travel from east (node 1) to west (node 8)? The network is shown in Figure 20. 31 Two Chaps and a Truck Movers have been hired to move the office furniture and equipment of Wray Properties to the company's new headquarters. What route do you recommend? The network of roads is shown in Figure 21. 32 A security firm needs to connect alarm systems to the firm's main control site from five potential trou- ble locations. Since the systems must be fail-safe, the cables must be run in special pipes. These pipes are very expensive but large enough to simultane- ously handle five cables (the maximum that might be needed). Use the minimal-spanning tree model to find the minimum total length of pipes needed to 3 FIGURE 19 Network for Problem 29: Coogan Construction 8 7 12 14 5 2. 3 3 5 2 5 6 6 6 13 4 4 3 lun 5 3 11 10 FIGURE 20 Network for Problem 30: Six Mile, South Carolina 2. 2 0 2 2 FIGURE 21 Network for Problem 31: Two Chaps and a Truck Movers New Office 100 120 100 50 100 130 100 50 3 40 8 13 40 20 200 100 100 100 100 Old Office 100 50 12