The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M. A B 21 D H 10 K M Which nodes are the origin and destination for this problem?
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- Solve the following case study using the transportation method:Suppose there is a manufacturing company that produces and distributes its products to various customer locations across the country. This company has three production plants (Plant A, Plant B, and Plant C) located in different locations, and there are also five distribution centers (DC 1, DC 2, DC 3, DC 4, and DC 5) scattered across various regions. Sources Distribution Center DC 1 DC 2 DC 3 DC 4 Capacity Plant A $145 $150 $165 $140 2000 Plant B $175 $135 $120 $165 1250 Plant C $113 $156 $134 $148 1250 Demand 1000 1200 1400 900 The company's goal is to determine the most efficient transportation routes for delivering products from the plants to the distribution centers, considering transportation costs and available capacities.a. A farmers' cooperative association plans to build a new sugar mill in Georgetown. The primary objective of the mill is to provide the farmers with a place to take their crop for processing that will reduce their transportation costs. The members of the co-op believe that the center-of-gravity method is appropriate for this objective. While there are over 200 sugar cane farms in the region, they are tightly clustered around six villages. Using the data below, use the center-of-gravity method to calculate the coordinates of the best location for this mill. All mileage references use Browns Town as (0,0). Village Barney Valley Blue Pasture Congo Valley Bower Rabacca Salem Miles East of Miles North of Sugar Cane Browns Town Browns Town 90 140 20 50 100 10 10 60 70 20 80 120 tonnage 240,000 320,000 450,000 120,000 60,000 140,000Travelling Salesman Problem (TSP); Given the following distance matrix, use the nearest neighbor (NN) heuristic to find a route that starts from the warehouse (W), visits each customer only once, and finishes at the warehouse to minimize the distance traveled. What is the route and the corresponding distance? Distances W 1 2 3 4 in miles 18 57 27 50 18 0 65 29 61 57 65 0 36 99 3 27 29 36 0 76 4 50 61 99 76 Route=W-1-3-2-4, Distance=182 miles Route=W-3-1-2-4-W, Distance=270 miles Route = W-3-1-2-4, Distance=220 miles Route=W-1-3-2-4-W, Distance=232 miles Route=W-1-3-4-2, Distance=272 miles 1, 2.
- A farmers' cooperative association plans to build a new sugar mill in Southwestern Louisiana. The primary objective of the mill is to provide the farmers with a place to take their crop for processing and then transport the processed crop to their customers. While there are over 200 sugar cane farms in the region, they are tightly clustered around a few villages. Using the data below, calculate the coordinates of the best location for this mill. All mileage references use the city of Lake Charles as (0,0). Sources/Markets Transportation Quantity Xn Yn Cost $/ton mile in Tons (Fn) (Dn) Supply Arceneaux Boudreaux Cancienne Market Darbonne Evangeline Fontenot 4.3 240,000 90 140 20 10 60 70 4.8 320,000 120,000 4.1 5.25 3.95 4.85 450,000 90,000 140,000 50 20 100 80 120 10 a) What is the cost to transport 10000 tons of material between Arceneaux and Darbonne locations? b) What is the optimal location for the mill? c) What is the minimal shipping cost that satisfies all requirements?Determine an initial basic feasible solution to the following transportation problem by using (a) NWCM, (b) LCM, and (c) VAM2. Unbalanced. Provide the transportation model for the calculation of cost given the following data: Use the Stepping Stone Method to solve the following. Use degeneracy method or dummy method if necessary.
- 2. The table below shows the cost matrix From – To- travel that must fulfil by PT. JauhAbadi marketing officer. Help the officer to determine the route from City A to all other cities with minimum cost Cities A C D E A M 16 18 13 20 B 21 M 16 27 14 C 12 14 M 15 21 D 11 18 19 M 21 E 16 14 17 12 M INSTRUCTION: Use handwriting and software to find solution of Problem 2. Screenshot each process to show how the problem solved.3. Figure 1 Daily Subway and Bus Use in Five Major Cities 0.75 0.5 0.25 Subway OBus London Tokyo Singapore Hong Kong Figure 2 Subway vs. Bus Ridership, New York City OBus Subway 1970 1980 1990 2000 2010 Information in figure I suggests that public transportation users in London Information in Figure I supports the author's point that buses are growing in popularity as a means of urban transport by indicating that A) take subways and buses at similar rates. B) are unusually reliant on buses. C) take at least one subway trip daily. D) take subways at about the same rate as people A) many people around the world take at least one bus trip every day. B) bus ridership surpasses subway ridership in some major cities. C) people in Tokyo make far more trips by bus daily than they do trips by subway. D) the number of bus trips taken by people in major cities has substantially increased. in New York. 2 Which of the following statements about bus use in New York City is best supported by…Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Factory/DCs Detroit Los Angeles Austin 1 2 3 Retailers/DCs Just Sports Sports 'N Stuff Iowa The Sports Dude 25.00 35.00 40.00 8 9 4 1 Shipping Costs ($ per skateboard) Iowa 30.00 27.50 Maryland 30.00 25.00 4 45.00 40.00 Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports…
- eBook Problem 10-31 A long-distance telephone company uses a fiber-optic network to transmit phone calls and other information between locations. Calls are carried through cable lines and switching nodes. A portion of the company's transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can be transmitted over that branch of the network. To keep up with the volume of information transmitted between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city located at node 1 to a oty located at node 7. 3 Maximum number of messages -9-39. Grey Construction would like to determine the leastexpensive way of connecting houses it is buildingwith cable TV. It has identified 11 possible branchesor routes that could be used to connect the houses.The cost in hundreds of dollars and the branches aresummarized in the following table.(a) What is the least expensive way to run cable tothe houses?1. Central Construction Company moves materials between three plants and three projects. Project A requires 72 truckloads each week, project B requires 102, and project C requires 41. Plant W can supply 56 loads, plant X can supply 82, and plant Y can supply 77. Using the cost information given in the following table, compute the optimum transportation cost using the stepping stone method. COST INFORMATION From To Project A To Project B To Project C Plant w P 4.00 8.00 8.00 Plant X 16.00 24.00 16.00 Plant Y 8.00 16.00 24.00