e. Use VAM to obtain the initial solution for the transportation model below: Minimize Z = (21x11 +16x12 + 25.x13 +13x14) + (17x21 +18x22 +14x23 + 23.x24) + (32x31 + 27x32 +18x33 +41x34) Subject to Capacity constraints X11 + X12 + X13 + x14 = 11 Requirement constraints X11 + x21 + X31 = 6 X21 + x22 + x23 +x24 = 13 X12 + x22 + x32 = 10 X31 +X32 + X33 +x34 = 19 X13 +x23 +X33 = 12 X14 +X24 + X34 = 15 and y 2 0, for all i = 1,2,3,4 ; j = 1,2,3
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- Explain how to determine the number of variables and constraints that would be in a transportation problem simplyby knowing the number of sources and the number of destinations.Luminous lamps have three factories - F1, F2, and F3 with production capacity 30, 50, and 20 units per week respectively. These units are to be shipped to four warehouses W1, W2, W3, and W4 with requirements of 20, 40, 30, and 10 units per week respectively. The transportation costs (in Rs.) per unit between factories and warehouses are given below. Find an initial basic feasible solution.The optimal solution to the original Grand Prix problem indicates that with a unit shipping cost of $132, the route from plant 3 to region 2 is evidently too expensive—no autos are shipped along this route. Use SolverTable to see how much this unit shipping cost would have to be reduced before some autos would be shipped along this route.
- The Child-fair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distribution centers is given below. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost, where the freight cost for each shipment is $100 plus 50 cents/mile? Formulate this case as a transportation problem (a) algebraically, and (b) on a spreadsheet, then (c) use Solver to obtain the optimal solutionsExplain in detail Consider a balanced transportation problem with the cost of transportation Cij given by: C11=10,C12=0,C13=20,C14=11C11=10,C12=0,C13=20,C14=11, C21=12,C22=7,C23=9,C24=20C21=12,C22=7,C23=9,C24=20 , C31=0,C32=14,C33=16,C34=18C31=0,C32=14,C33=16,C34=18, with the current basic feasible solution (BFS): x12=15,x22=0,x23=15,x24=10,x31=5,x34=0x12=15,x22=0,x23=15,x24=10,x31=5,x34=0. Then Select one: a)current solution is not optimal and x24x24 is a leaving variable b)None of these c)the current BFS is optimal d)current solution is not optimal and x23x23 is a leaving variableA person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.
- A company has three manufacturing plants (in Atlanta,Tulsa, and Springfi eld) that produce a product that is then shipped to one of four distribution centers. Th e three plants can produce13, 18, and 12 truckloads of product each week, respectively. Eachdistribution center needs 10 truckloads of product each week. Th eshipping costs per truckload between the plants and distributioncenters are given in the table. Th e company needs to determinehow much to ship from each plant to each distribution center andwould like to minimize total shipping costs (a) Formulate an LP to minimize the total shipping costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolutionJefferson Distributing is analyzing distribution networks with either 4, 5, 6 or 7 warehouses to serve 200 major customers in Europe. Relevant costs include transportation cost from the warehouses to customers, fixed facility costs, and inventory costs in the warehouses. The table below shows the annual transportation cost produced by a facility location software tool for locating 4, 5, 6 or 7 warehouses for this company. Suppose that annual inventory cost for the network can be modeled as $800,000 times the square root of the number of warehouses. Thus, if the network has 4 warehouses, then the annual inventory cost would be $800,000 x √4= $1,600,000. Number of Warehouses Transportation Cost 4 8,000,000 5 6,500,000 6 5,000,000 7 4,400,000 a) If the annual fixed cost per warehouse is $1,000,000, how many warehouses should there be to minimize the total (transportation + warehouse + inventory) cost? b) Now suppose the…The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for 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 quickest option to travel from city A to city J. What is the shortest time possible to travel from node F to node J. Multiple Choice: 200 140 110 180 160
- The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69 (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations. Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…TRANSPORTATION METHOD: INSTRUCTIONS: Solve for the optimal distribution and cost of transportation using the given problem below. Show all solution. GIR Company received a contract to supply unleaded gasolne to four different locations Project A needs 60,000 iters, Project Bneeds 90,000 liters, Project Oneeds 20,000 liters, and Product D needs 30,000 liters. The company has two depot located in two different places, Depot 1 har 220.000 liters available and Depot 2 has 80,000 sters wal sole. Cost to Transport Project Project B Project C Proxecto 5 7 13 Depot 1 Depot 2 8 6 B B SIMPLEX METHOD: Instruction Detamine the optimal solution Mimiz 50XL -20 X2 Subject to X1 420 X1 X2 248Fairway Inc. makes custom golf clubs. They are manufactured in 3 plants in Denver, Phoenix, and Dallas. They are then shipped to distribution centers in Sacramento, Salt Lake, Chicago, Albuquerque, and New York. Since shipping costs are a major expense, management requires an analysis to determine the optimal shipping routes and quantities shipped along those routes. Each plant has a maximum production capacity and each distribution center has a demand that must be satisfied. You must determine how many clubs to send along each route, staying within plant capacity, meeting demand, for the lowest total shipping cost. Shipping Costs per route Plants Sacramento Salt Lake Chicago Albeq New York Capacity Denver $10 $8 $6 $5 $4 310 Phoenix $6 $5 $4 $3 $6 260 Dallas $3 $4 $5 $5 $9 280 Demand 180 80 200 160 220 Number to ship from plant to warehouse: Plants Sacramento Salt Lake Chicago Albeq New York Total Shipped Denver Phoenix…