Consider the network below. Formulate the LP model for finding the shortest route path from node 1 to node 7. Consider the arcs between the transnodes (2-6) as two-way and travel times are shown on the arcs. 11 18 21 14 13 xt 24 H 15 22 Please indicate the model first (objective function and the constraints) below then place into LINDO for optimal solution Indicate the shortest-route path and objective value (distance) below. Show all work for credit.
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- Consider the following transshipment network for finding the shortest route from node 1 to node 7. Min s.t. Node 1 Flows X12 +*13 Node 3 Flows Node 4 Flows Node 5 Flows 18 Node 6 Flows Node 7 Flows w +x14 X Node 2 Flows -x12 - x32-x52 + x23+x25 = 0 3 4 (a) Formulate a linear programming model of the problem. (Express your answers using Xij, where each x¡¡ is either 0 or 1 for the arc from node i to node j.) 5 4 3 6 3 6 7All-Weather Oil and Gas Company is planning delivery routes to six natural gas customers. The customer locations and gas requirements (in gallons) are given in the following table. (given) Assume that the depot is located at the origin of the grid and that the delivery trucks have a capacity of 1,200 gallons. Also assume that the cost of travel between any two locations is the straight-line (Euclidean) distance between them. Find the route schedule obtained from the savings method.Consider the transportation problem having the following data: c) write the algebraic formulation of this problem.
- The MidLands Trucking Company based in Louisvillehas eight trucks located throughout the Mideast that havedelivered their loads and are available for shipments. Through their Internet logistics site MidLands has re-ceived shipping requests from 12 customers. The follow-ing table shows the mileage for a truck to travel to a customer location, pick up the load, and deliver it. Determine the optimal assignment of trucks to customersthat will minimize the total mileage. Customers Truck A B C D E F G H I J K L1 500 730 620 410 550 600 390 480 670 710 440 5902 900 570 820 770 910 660 650 780 840 950 590 6703 630 660 750 540 680 750 810 560 710 1200 490 6504 870 1200 810 670 710 820 1200 630 700 900 540 6205 950 910 740 810 630 590 930 650 840 930 460 5606 1100 860 800 590 570 550 780 610 1300 840 550 7907 610 710 910 550 810 730 910 720 850 760 580 6308 560 690 660 640 720 670 830 690 880 1000 710 680La Vie Sdn Bhd owns five book cafes and four bakeries. Table 1a shows the location, monthly supply and demand between the bakeries and the cafes. Table 1b provides the transportation cost from the bakeries to the cafes. Determine the minimum cost bearable by the company by applying the North-West Corner method. Optimise the solution using the Stepping Stone Method. Bakery location/ Lokasi bakeri Cheras Sentul Bangsar Kelana Jaya Bakery location/ Lokasi bakeri Cheras Sentul Bangsar Kelana Jaya Monthly supply/ Bekalan bulanan Arissa (RM) 11 7 2 Table la 120 180 100 120 Table 1b La Mere Tiramisu (RM) 15 9 5 5 Cafe / Kafe Arissa La Mere Tiramisu Riviere Mer Solve a Transportation Problem using the > i) The North West Method ii) The Stepping Stone Method (RM) 9 7 7 7 Monthly demand/ Permintaan bulanan Riviere (RM) 7 12 150 120 100 90 60 Mer (RM) 10 14 16 20A new stadium complex is being planned for Denver, and the Denver traffic engineer is attempting to determine whether the city streets between the stadium complex and the interstate highway can accommodate the expected flow of 21,000 cars after each game. The various traffic arteries between the stadium (node 1) and the interstate (node 8) are shown in the following 1 10 8 7 0 1 LO 5 0 N 3 3 4 CO 6 6 LO 5 4 5 0 0 0 2 LO 6 26 2 7 8 4 9 0 0 8 The flow capacities on each street are determined by the number of available lanes, the use of traffic police and lights, and whether any lanes can be opened or closed in either direction. The flow capacities are given in thousands of cars. Determine the maximum traffic flow the streets can accommodate and the amount of traffic along each street. Will the streets be able to handle the expected flow after a game? Hint: I would use LP to solve it.
- Given the following transportation matrix where the numbers in the cells represent cost of transporting 1unit from a specific source to a specific destination, determine the initial solution using the 3 methods anddetermine the optimum solution by using the initial solution with the lowest value of Z.4. The plant engineer for the Bitco manufacturing plant is designing an overhead conveyor system that will connect the distribution/inventory center to all areas of the plant. The network of possible conveyor routes through the plant, with the length (in feet) along each branch, follows 120 160 80 50 210 140 4 190 40 130 50 6 Determine the shortest conveyor route from the distribution/inventory center at node 1 to each of the other six areas of the plant.1. Frieda Millstone and her family live in Roanoke, Virginia, and they are planning an auto vacation across Virginia, their ultimate destination being Washington, DC. The family has developed the following network of possible routes and cities to visit on their trip: Winchester 5 Washington, DC 2 Staunton Charlottesville 2 3 3 2 Richmond Roanoke The time, in hours, between cities (which is affected by the type of road and the number of intermediate towns) is shown along each branch. Determine the shortest route that the Millstone family can travel from Roanoke to Washington, DC.3. 2)
- National Express Parcel Service has established various truck and air routes over which it ships parcels. The holiday season is approaching, which means a dramatic increase in the number of packages that will be sent. The service wants to know the maximum flow of packages it can accommodate (in tons) from station 1 to station 7. The network of routes and the flow capacities (in tons of packages per day) along each route are shown in the following network: 3 6 1 2 5 3 5 7 4 Use the Ford-Fulkerson algorithm for maximal flow to determine the maximum tonnage of packages that can transported per day from station 1 to station 7. Find the flow along each arc. 2 2 2 6 3 - 4 2 50Cars-to-Dealers Logistics Inc. is the exclusive logistics provider for the Summit Motor Co. and has responsibilityfor transporting cars from Summit’s 3 manufacturing plants in Toledo, OH; Charlotte, NC and Savannah, GA tothe 7 regional dealer locations as in the tables provided in your dataset. To do this, Cars-to-Dealers uses threetransshipment facilities and all cars in the distribution network pass through these transshipment facilities.Dataset also contains the information about the capacities of each of these transshipment facilities, the demandrequirement at each of the regional dealer locations and the unit cost to ship one car between the variouslocations.In addition to supply of cars (manufacturers) and demand for cars (dealers) there are two types of constraintsfor each transshipment facility:1. Balance flow constraints: dictate that all cars flowing into a transshipment facility should also flow out of thetransshipment facility – i.e. no inventory of cars should remain at…John Clooney, a bush pilot in Alaska, makes regular charter flights in his floatplane to various towns and cities in western Alaska. His passengers include hunters, fishermen, backpackers and campers, and tradespeople hired for jobs in the different localities. He also carries some cargo for delivery. The following network shows the possible air routes between various towns and cities John might take (with the times, in hours). For safety reasons, he flies point-to-point, flying over at least one town along a route, even though he might not land there. In the upcoming week John has scheduled charter flights for Kotzebue, Nome, and Stebbins. Determine the shortest route between John’s home base in Anchorage and each of these destinations.