Given the following transportation matrix where the numbers in the cells represent cost of transporting 1 unit from a specific source to a specific destination, determine the initial solution using the 3 methods and determine the optimum solution by using the initial solution with the lowest value of Z. From/To 3 4 5 6 Dummy | Supply 40 35 M M 100 60 45 M M 200 3 12 20 M 300 4 15 10 30 300 5 M M 15 300 Demand 300 300 | 300 | 150 150 1,200
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- 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.PLEASE 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…Suppose the company has received a proposal for setting up another warehouse(Warehouse E) with a capacity of 900 units. The location of the warehouse is such thatthe unit costs of transporting to the six cities are as follows: Hyderabad–45, Mysore–75, Chennai–30, Kochi–65, Pune–90 and Vizag–80. The company would like to knowhow the allocation will change if the warehouse is made operational and the likely costimpact on the operation of the system. After balancing above table by which method we should solve this problem
- Suppose there is a transportation model with 4 factories and 6 warehouses. In order to develop an initial solution using the intuitive lowest cost method, do we have to add one or more dummy sources in the transportation matrix, and why?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…given 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?
- 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 25Consider the transportation table below. REQUIRED:(a) Use the Northwest-Corner Method, the Least-Cost Method and the VAM to get the starting feasible solution.(b) Find the optimal solution by considering the smallest value of the objective function computed in (a).A garment producer has three warehouses W1, W2, and W3. These warehouses have 30, 60, and 70 units of their items. Their five retail showrooms at R1, R2, R3, R4, and R5 need 35, 20, 40, 28, and 12 units respectively. Determine the optimum distribution cost. The transport cost in ($ per unit) between every warehouse and every retail showroom is presented in the below table: Warehouse Retail Showroom R1 R2 R3 R4 R5 W1 55 30 40 50 40 W2 35 30 100 45 60 W3 40 60 95 35 30
- 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.Tommy Hilfiger is currently considering to source certain textile goods, Tommy Jeans, from Mexico. The estimated shipping time from Mexico to the U.S. for each shipment of Tommy Jeans is 4 days and the estimated freight cost of each shipment is $800. On the other hand, the current average shipping time from Vietnam to the U.S. for each shipment of Tommy Jeans is 23 days and the average freight cost is $2300. Even though the shipping time and freight cost seem to be much lower in case of Mexico, Tommy Hilfiger management is concerned about the production cost of each Jeans shipment. The management anticipates that the production cost of each Jeans shipment will be higher in Mexico compared to Vietnam. However, Tommy Hilfiger management has decided that even if the total cost (sum of production cost, freight cost, and holding cost) remain similar to Vietnam, Tommy Hilfiger will still source Jeans from Mexico because of the reduced shipping time, which, in turn, will result in better…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 0 0 1 0…