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Optimal Prime is leading its group of AMPLbots into battle against Gigatron and the Deceivacons, fighting for the planet Psybertron. (No relation to any existing franchises, toys or movies with bad plots). Optimal Prime needs to place its troops at a number of bases, where they will be teleported to each outpost where they are needed. Each outpost has a number of required troops, and each base can only support a certain number of troops. The cost in energy of transporting a single bot from a base to an outpost is given in the map. Due to battle damage, some of the teleportation links are not working, so only the arcs shown on the map are usable. Each base also has an energy cost for each bot stationed there. Being very optimal, Optimal Prime wants to place its troops in a way that uses the least energy. Where should the troops be stationed? What would be the optimal total cost of Optimal Prime? In the diagram, bases are denoted as squares and outposts as circles. Capacity: 250 Unit cost: 20 Capacity: 300 Unit cost: 25 4 Capacity: 100 Unit cost: 10 15 20 3 Capacity: 200 Unit cost: 15 20 A Demand: 150 10 15 25 20 Demand: 100 Demand: 175 B Demand: 125 10 D Demand: 150

Optimal Prime is leading its group of AMPLbots into battle against Gigatron and the Deceivacons, fighting for the planet Psybertron. (No relation to any existing franchises, toys or movies with bad plots). Optimal Prime needs to place its troops at a number of bases, where they will be teleported to each outpost where they are needed. Each outpost has a number of required troops, and each base can only support a certain number of troops. The cost in energy of transporting a single bot from a base to an outpost is given in the map. Due to battle damage, some of the teleportation links are not working, so only the arcs shown on the map are usable. Each base also has an energy cost for each bot stationed there. Being very optimal, Optimal Prime wants to place its troops in a way that uses the least energy. Where should the troops be stationed? What would be the optimal total cost of Optimal Prime? In the diagram, bases are denoted as squares and outposts as circles. Capacity: 250 Unit cost: 20 Capacity: 300 Unit cost: 25 4 Capacity: 100 Unit cost: 10 15 20 3 Capacity: 200 Unit cost: 15 20 A Demand: 150 10 15 25 20 Demand: 100 Demand: 175 B Demand: 125 10 D Demand: 150

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 61P
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Optimal Prime is leading its group of AMPLbots into battle against Gigatron and the Deceivacons, fighting for the planet Psybertron. (No relation to any existing franchises, toys or movies with bad plots). Optimal Prime needs to place its troops at a number of bases, where they will be teleported to each outpost where they are needed. Each outpost has a number of required troops, and each base can only support a certain number of troops. The cost in energy of transporting a single bot from a base to an outpost is given in the map. Due to battle damage, some of the teleportation links are not working, so only the arcs shown on the map are usable. Each base also has an energy cost for each bot stationed there. Being very optimal, Optimal Prime wants to place its troops in a way that uses the least energy. Where should the troops be stationed? What would be the optimal total cost of Optimal Prime? In the diagram, bases are denoted as squares and outposts as circles. 1 Capacity: 250 Unit cost: 20 2 Capacity: 300 Unit cost: 25 Capacity: 100 Unit cost: 10 15 20 3 Capacity: 200 Unit cost: 15 20 A Demand: 150 10 15 25 20 C Demand: 100 E Demand: 175 Demand: 125 10 D Demand: 150
Transcribed Image Text:Optimal Prime is leading its group of AMPLbots into battle against Gigatron and the Deceivacons, fighting for the planet Psybertron. (No relation to any existing franchises, toys or movies with bad plots). Optimal Prime needs to place its troops at a number of bases, where they will be teleported to each outpost where they are needed. Each outpost has a number of required troops, and each base can only support a certain number of troops. The cost in energy of transporting a single bot from a base to an outpost is given in the map. Due to battle damage, some of the teleportation links are not working, so only the arcs shown on the map are usable. Each base also has an energy cost for each bot stationed there. Being very optimal, Optimal Prime wants to place its troops in a way that uses the least energy. Where should the troops be stationed? What would be the optimal total cost of Optimal Prime? In the diagram, bases are denoted as squares and outposts as circles. 1 Capacity: 250 Unit cost: 20 2 Capacity: 300 Unit cost: 25 Capacity: 100 Unit cost: 10 15 20 3 Capacity: 200 Unit cost: 15 20 A Demand: 150 10 15 25 20 C Demand: 100 E Demand: 175 Demand: 125 10 D Demand: 150
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