13.4 Trees 887 c) If the cost of installing wiring on the sculpture is $2.75 per inch, determine the minimum cost for wiring this sculpture. $200.75 27. Commuter Train System Several communities in eastern Pennsylvania wish to establish a commuter rail train system between the cities shown in the following map (distances are in miles). 82 44 57 33 60 59 72 96 37 25 25 Harrisburg Allentown Philadelphia York Reading Lancaster a) Use Kruskal’s algorithm to determine the minimumcost spanning tree that would link the cities using the shortest distance. * b) If it costs $1,300,000 per mile of railroad track, how much does the commuter rail system determined in part (a) cost? $241,800,000 28. Linking Campuses Five of the campuses in the University of Texas system would like to establish a high-speed telephone and data network between the campuses. The campuses are located in the following cities: Brownsville, Dallas, El Paso, San Antonio, and Tyler. The following map gives the approximate distances in miles between these five campuses. Dallas San Antonio 831 537 333 548 278 275 734 553 636 98 Tyler Brownsville El Paso a) Use Kruskal’s algorithm to determine the minimumcost spanning tree that would link the five campuses to create the telephone and data network with the shortest distance. * b) If it costs $2500 per mile to install the network, how much will it cost to produce the network determined in part (a)? $3,010,000 29. Horse Trails The Darlington County, South Carolina, tourism office wishes to build a horse trail that connects the towns of Darlington, Hartsville, Lamar, and Society Hill. The distances, in miles, between these cities are given in the following table. Darlington Hartsville Lamar Society Hill Darlington * 12 14 15 Hartsville 12 * 13 16 Lamar 14 13 * 26 Society Hill 15 16 26 * a) Use Kruskal’s algorithm to determine the minimumcost spanning tree that would link each city to create the least expensive horse trail. * b) If the cost of building such a trail is $11,500 per mile, what would be the cost of building the trail determined in part (a)? $460,000 30. Bicycle Trails The Ohio Recreation Council is interested in creating bicycle trails connecting the following cities: Akron, Cleveland, Dayton, Toledo, and Youngstown. The distances, in miles, between these cities are given in the following table. Akron Cleveland Dayton Toledo Youngs- town Akron * 37 226135 57 Cleveland 37 * 240123 69 Dayton 226 240 * 163 265 Toledo 135 123 163 * 184 Youngstown 57 69 265 184 * a) Use Kruskal’s algorithm to determine the minimumcost spanning tree that would link each city and create the shortest total distance for the bicycle trails. * b) If the cost of building bicycle trails is $13,000 per mile, what would be the cost of building the trails determined in part (a)? $4,940,000 31. Recreation Trail The Missouri Park and Recreation Association would like to build a recreation trail for biking and hiking that connects the cities of Jefferson City, Kansas City, Springfield, St. Joseph, and St. Louis. The distances in miles between these cities are given in the following table. *See Instructor Answer Appendix Ahturner/Shutterstock
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