The supplies, demands, and transportation costs per unit are shown on the network. The optimal (cost minimizing) distribution plan is given below. (Assume X11 = amount shipped from Jefferson City to Des Moines, X12 = amount shipped from Jefferson City to Kansas City, X13 = amount shipped from Jefferson City to St. Louis, X21 = amount shipped from Omaha to Des Moines, X22 = amount shipped from Omaha to Kansas City, and X23= amount shipped from Omaha to St. Louis.) Des Moines Kansas City St. Louis Supply Jefferson City Omaha Demand 38 23 61 0 51 51 46 0 46 84 74 Use the procedure described in Section 12.7 to try to find an alternative optimal solution. (Round your answers to the nearest integer.) (X11 X12′ 13′ X21 ×22×23) = (0, 38, 46, 61,
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- 4. Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Set up the solution in Excel and solve with Solver. What are total costs?(b)Consider a transportation model with m sources and n destinations. Describe briefly how you can resolve the following situations while solving the problem: (i) Total supply is greater than total demand,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.
- 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 company has three existing warehouses to which it will ship furniture from a new factory whose location must be decided. The factory will receive raw materials from its wood supplier and fabric supplier. The annual number of shipments, shipment costs and the location of the suppliers and warehouses are shown below Existing facilities Annual L to or from fact cost Coordinate location Wood supplier 120 10 (100, 400) Fabric supplier 200 10 (800,700) Ware h 1 61 10 (300, 600) Ware h 2 40 10 (200, 100) Ware h 3 70 10 (600, 200) Using the median load answer the following questions –Where the factory should be located to minimize annual transportation cost –What will be the minimum annual transportation costQn1. Find the optimal solution to the transportation problem using MODI method. Warehouses Supply WI W2 W3 W4 P1 19 30 50 12 Plants 5. 2. P2 70 30 40 60 P3 40 10 60 20 3. 15 Demand 4)
- 1. Central Construction Company moves materials between three plants and three projects. Project A requires 140 truckloads each week, project B requires 200, and project C requires 80. Plant W can supply 120 loads, plant X can supply 160 , and plant Y can supply 140. Using the cost information given in the following table, compute the optimal transportation cost using the stepping-stone method. Cost Information From To project A To project B To project C Plant W $10 $4 $9 Plant X 6. 5 Plant Y 7 4The objective function of a transportation problem is to: A. maximize transportation cost B. maximize supply quantities C. minimize total shipping cost D. minimize total demand Don't answer by pen paper and don't use chatgpt otherwise we will give dounvoteTRANSPORTATION . Given the following transport. tion 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. 3 4 40 35| M M 20 30 From/To 5 6 Dummy | Supply 1 M 100 60 45 M 200 3 12 M 300 4 15 10 300 5 M M 15 300 Demand 300 300 300 | 150 150 1,200
- Using the intuitive least cost method for the given transportation problem, answer the following: Cleveland Dayton Erie Supply Allentown $22 $16 $21 100 Philadelphia $28 $27 $18 150 Harrisburg Demand $25 $23 $19 175 175 175 175 What is the maximum quantity that can be shipped from Allentown to Erie? [ Select] What is the maximum quantity that can be shipped from Harrisburg to Cleveland? [ Select] What is the maximum quantity that can be shipped from Harrisburg to Dayton? [ Select ] Which demand location will have an unmet demand? [Select ]Draw the network for this transportation problem. (Let X;; represent the flow from node i to node j.) Xij 300 1 300 2 O Min 2x13 + 4x14 + 4X15 + 10x23 + 11x24 + 11x25 s.t. 11 11 10 4. 4 2 X13X14 + X15 ≤ 500 X23 + x24 + X25 ≤ 400 X13 + x23 = 300 X14 +*24 = 300 X15 + 25 = 300 Xij 20 3 300 4 400 5 500 300 1 11 300 2 300 3 11 10 4 4 2 4 400 500 1 5 500 400 2 2 4 4 10 11 11 3 300 4 300 5 300 500 1 2 400 2 300 3 4 10 11 11 4 300 5 300Consider the following transportation decision-making information: Plant Capacity Store Demand A 400 X 200 B 500 Y 250 C 100 Z 300 Total 1000 Total 750 Cost to ship from plant to store (per unit of demand) Plant Store X Y Z A $2 $2 $3.5 B $4 $5 $4.5 C $3 $3 $3 A. Develop the following shipping assignment table that uses the Solver function to find the optimal shipping patterns between the plants and the stores. Plant Store X Y Z A B C B. What is the minimal shipping cost?