Variable Cost and Following Table
EM 505 - Decision Models, Fall 2012 Homework 3 - December 10-11, 2012
1. The diagram below depicts a system of aqueducts that originate at three rivers (nodes R1, R2 and R3) and terminate at a major city (node T) where the other nodes are junction points in the system. Using units of thousands of acre feet, the tables below show the maximum amount of water that can be pumped through each aqueduct per day and the following diagram shows the network of the system. From/To A R1 75 R2 40 R3 B 65 50 80 C 60 70 From/To D A 60 B 70 C E 45 55 70 F 45 90 From/To T D 120 E 190 F 130
The city water manager wants to determine a flow plan that will maximize the flow of water of the city. Formulate this problem as a max flow problem by identifying a source, a sink and transshipment nodes, and then drawing the complete network that shows the capacity of each arc. 2. The Quick Chip gravel company has received a contract to supply two new construction projects in the towns of Brock and Wurst. A total of 60 truckloads are needed at Brock in the next month and 90 at Wurst. Quick Chip has idle gravel pits in the towns of Nova, Scova, and Tova, each with a monthly production capacity of 50 truckloads. Travel distances from each pit to each project site are shown in the following table: Pit Nova Scova Tova To Brock 23 8 53 To Wurst 77 94 41
The truck company wants to fulfill its contract at least total truck travel distance. Formulate an LP to choose an optimal shipping plan. 3. The Makonsel Company is a fully integrated company that both produces goods and sells them at its retail outlets. After production, the goods are stored in the company’s two warehouses until needed by the retail outlets. Trucks are used to transport the goods from two plants to the warehouses, and then from the warehouses to the three retail outlets. Using the units of full truckloads, the following table shows each plant’s monthly output, its shipping cost per truckload sent to each warehouses, and the
1. The diagram below depicts a system of aqueducts that originate at three rivers (nodes R1, R2 and R3) and terminate at a major city (node T) where the other nodes are junction points in the system. Using units of thousands of acre feet, the tables below show the maximum amount of water that can be pumped through each aqueduct per day and the following diagram shows the network of the system. From/To A R1 75 R2 40 R3 B 65 50 80 C 60 70 From/To D A 60 B 70 C E 45 55 70 F 45 90 From/To T D 120 E 190 F 130
The city water manager wants to determine a flow plan that will maximize the flow of water of the city. Formulate this problem as a max flow problem by identifying a source, a sink and transshipment nodes, and then drawing the complete network that shows the capacity of each arc. 2. The Quick Chip gravel company has received a contract to supply two new construction projects in the towns of Brock and Wurst. A total of 60 truckloads are needed at Brock in the next month and 90 at Wurst. Quick Chip has idle gravel pits in the towns of Nova, Scova, and Tova, each with a monthly production capacity of 50 truckloads. Travel distances from each pit to each project site are shown in the following table: Pit Nova Scova Tova To Brock 23 8 53 To Wurst 77 94 41
The truck company wants to fulfill its contract at least total truck travel distance. Formulate an LP to choose an optimal shipping plan. 3. The Makonsel Company is a fully integrated company that both produces goods and sells them at its retail outlets. After production, the goods are stored in the company’s two warehouses until needed by the retail outlets. Trucks are used to transport the goods from two plants to the warehouses, and then from the warehouses to the three retail outlets. Using the units of full truckloads, the following table shows each plant’s monthly output, its shipping cost per truckload sent to each warehouses, and the