Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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For the weighted graph, find the cheapest link tour.
### Exercises on Finding the Cheapest-Link Tour #### 49. Find the cheapest-link tour (and give its cost) for the furniture truck TSP discussed in Exercise 29 (see Fig. 6-39). #### 50. Find the cheapest-link tour for the social worker TSP discussed in Exercise 30 (see Fig. 6-40). #### 51. For the Brute-Force Bandits concert tour discussed in Exercise 37, find the cheapest-link tour, and give the bus cost for this tour (see Fig. 6-43). #### 52. **Cheapest-Link Tour for a Weighted Graph** For the weighted graph shown in Fig. 6-47, find the cheapest-link tour. Write the tour using \( B \) as the starting vertex. **Figure 6-47: Weighted Graph** ![Weighted Graph](link-to-figure) This graph is comprised of 5 vertices: \( A \), \( B \), \( C \), \( D \), and \( E \). The weights of the edges (distances between the vertices) are as follows: - \( AB = 3.2 \) - \( AC = 3.6 \) - \( AD = 4.1 \) - \( AE = 3.4 \) - \( BC = 4.5 \) - \( BD = 2.4 \) - \( BE = 3.8 \) - \( CE = 3.3 \) - \( CD = 2.2 \) - \( DE = 3.1 \) The goal is to determine the tour with the smallest total weight, starting from vertex \( B \). #### 53. For Darren’s sales trip problem discussed in Exercise 41, find the cheapest-link tour, and give the total cost for this tour (see Fig. 6-45). #### 54. For the Platonic Cowboys concert tour discussed in Exercise 42, find the cheapest-link tour, and give the total mileage for this tour (see Fig. 6-46). #### 55. A rover on the planet Mercuria has to visit six sites labeled \( A \) through \( F \). Figure 6-48 shows the time (in days) for the rover’s tour.
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Transcribed Image Text:### Exercises on Finding the Cheapest-Link Tour #### 49. Find the cheapest-link tour (and give its cost) for the furniture truck TSP discussed in Exercise 29 (see Fig. 6-39). #### 50. Find the cheapest-link tour for the social worker TSP discussed in Exercise 30 (see Fig. 6-40). #### 51. For the Brute-Force Bandits concert tour discussed in Exercise 37, find the cheapest-link tour, and give the bus cost for this tour (see Fig. 6-43). #### 52. **Cheapest-Link Tour for a Weighted Graph** For the weighted graph shown in Fig. 6-47, find the cheapest-link tour. Write the tour using \( B \) as the starting vertex. **Figure 6-47: Weighted Graph** ![Weighted Graph](link-to-figure) This graph is comprised of 5 vertices: \( A \), \( B \), \( C \), \( D \), and \( E \). The weights of the edges (distances between the vertices) are as follows: - \( AB = 3.2 \) - \( AC = 3.6 \) - \( AD = 4.1 \) - \( AE = 3.4 \) - \( BC = 4.5 \) - \( BD = 2.4 \) - \( BE = 3.8 \) - \( CE = 3.3 \) - \( CD = 2.2 \) - \( DE = 3.1 \) The goal is to determine the tour with the smallest total weight, starting from vertex \( B \). #### 53. For Darren’s sales trip problem discussed in Exercise 41, find the cheapest-link tour, and give the total cost for this tour (see Fig. 6-45). #### 54. For the Platonic Cowboys concert tour discussed in Exercise 42, find the cheapest-link tour, and give the total mileage for this tour (see Fig. 6-46). #### 55. A rover on the planet Mercuria has to visit six sites labeled \( A \) through \( F \). Figure 6-48 shows the time (in days) for the rover’s tour.
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