1. a) Consider the following maximization transportation problem. Find the optimal solution and value. b) Do a sensitivity analysis on C12 Origin 1 2 3 4 Demand 12 13 5 8 1 80 13 17 6 12 Destination 2 120 11 8 4 3 3 70 Dummy Supply 0 0 0 0 50 320 100 150 40 30 320
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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.Draw the network for this transportation problem. (Let xij represent the flow from node i to node j.) Min 2x13 + 4x14 + 6x15 + 8x23 + 11x24 + 9x25 s.t. x13 + x14 + x15 ≤ 500 x23 + x24 + x25 ≤ 400 x13 + x23 = 300 x14 + x24 = 300 x15 + x25 = 300 xij ≥ 0PLEASE SHOW ALL FORMULA PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1…
- 1. Transportation Problem: The Navy has 9,000 pounds of material in Albany, Georgia that it wishes to ship to three installations: San Diego, Norfolk, and Pensacola. They require 4,000, 2,500, and 2,500 pounds, respectively (Destination or Demand amounts). Government regulations require equal distribution of shipping among the three carriers (Supply nodes). Note: This means the supply is the same for each type of transportation. The shipping costs per pound for truck, railroad, and airplane transit are shown below. Formulate and solve a linear program to determine the shipping arrangements (mode, destination, and quantity) that will minimize the total shipping cost.DestinationMode San Diego Norfolk PensacolaTruck $12 $ 6 $ 5Railroad 20 11 9Airplane 30 26 28 2. Transshipment Problem The Northside and Southside facilities of Zeron Industries supply three…ASAP PLEASE.. The distribution of goods from the source (factory) to the target (warehouse) will cause problems regarding TRANSPORT, namely how the goods are sent from the factory to the warehouse which produces minimum costs. If it is known that - the capacity of 3 factories is 40000, 30000 and 20000, - the need for 3 warehouses is 20000, 50000 and 30000 respectively. The cost of shipping goods from the factory to the warehouse is shown in the following table Solve the above TRANSPORTATION problems with VAM and MODITRANSPORTATION 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 248
- a. set up the transportation tableau for this problem, determine the initial solution using VAM and compute total cost b. solve using MODI c. are there multiple optimal solition? explain, if there are alternative solution, identify them d. formulate this problem as a linear programming modelGeneral Ford produces cars at L.A. and Detroit and hasa warehouse in Atlanta; the company supplies cars tocustomers in Houston and Tampa. The cost of shipping a carbetween points is given in Table 60 (“—” means that ashipment is not allowed). L.A. can produce as many as1,100 cars, and Detroit can produce as many as 2,900 cars.Houston must receive 2,400 cars, and Tampa must receive1,500 cars.a Formulate a balanced transportation problem thatcan be used to minimize the shipping costs incurred inmeeting demands at Houston and Tampa.b Modify the answer to part (a) if shipments betweenL.A. and Detroit are not allowed.c Modify the answer to part (a) if shipments betweenHouston and Tampa are allowed at a cost of $5.Consider the following transportation problem: Destination company A B C Supply 1 5 1 7 10 2 6 4 6 80 3 3 2 5 15 Demand 75 20 50 Since there is not enough supply, some of the demands at these destinations may not be satisfied. Suppose these are penalty costs for every unsatisfied demand unit which are given by 5, 3, and 2 for destination A, B, and C respectively. 1. Determine how many units and from which source needs to be shipped using the following methods: A) NWCB) LCMC) VAM2. Find the minimum distribution cost
- a.Find the starting solution of this transportation model by Least Cost Method. (Unit transportation costs are given in the table) Then find the optimal solution of this transportation model by Stepping Stone Method. D1 D2 D3 D4 Supply M1 16 24 14 11 25 M2 21 18 17 9 30 M3 15 13 21 14 40 Demand 25 25 20 25given the transportation problem, assume that the demands at the 4 destinations are 5, 5, 7, and 8 units, respectively, and the supplies at the 4 sources are 7, 3, 7 and 8 units, respectively.C₁₁=7ㅤ C₁₂=9ㅤ C₁₃ = 1ㅤ C₁₄ = 10 C₂₁= 22ㅤ C₂₂ = 25ㅤ C₂₃ = 16ㅤ C₂₄ = 26 С₃₁ = 28ㅤ C₃₂ = 32ㅤ C₃₃ = 24ㅤ Сз₄ = 32 C₄₁ = 12ㅤ C₄₂ = 14ㅤ C₄з = 6ㅤ C₄₄ = 16where m=4, n=4what is the optimal solution using vogel's approximation method, least-cost method, and northwest-corner rule?The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per month for cleaning their long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and 60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is shown in the following table: Distribution Center Wholesaler A B C D 1 $1.30 $1.40 $1.80 $1.60 2 $1.30 $1.50 $1.80 $1.60 3 $1.60 $1.40 $1.70 $1.50 a. Determine the optimal solution. Show that all capacities have been exhausted and that all demands can be met with this solution. b. What is the total cost of the solution?