Consider the following network representation of a transportation problem. 25 Des Moines 14 Jefferson 40 City Kansas 15 City 11 25 Omaha 24 St. Louis 25 Supplies Demands The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your model.
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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 X;; represent the flow from node i to node j.) Min 2x13 + 4x14 + 4X15 + 10X23 + 11x24 + 11x25 s.t. X13 + X14 + X15 ≤ 500 X23 + x24 + X25 ≤ 400 X13 + x23 300 X14 + X24 300 X15 + X25 300 = = =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?
- (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,A 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.b) The Scott Tractor Company ships tractor parts from Omaha to St. Louis by railroad. However, a contract limits the number of railroad cars the company can secure on each branch/arc during a week. Given these limiting conditions, the company wants to know the maximum number of railroad cars containing tractor parts that can be shipped from Omaha to St. Louis during a week. Phoenix Des Moines 3 5 6. 6. 1. Dallas 2 Omaha St. Louis 7. 3 Denver 6. ActivateW O 31°C
- a) Define the Transportation model. b) A Power company has three plants that supply the need of three cities. Each plant can supply the following numbers of kWh of electricity. Plants 1, 2 and 3 can supply 30, 40 and 50 million kWh respectively. The demand at City 1, City 2 and City 3 are 20, 40 and 40, respectively. Table 1 shows the cost of sending electricity from each plant to each city depends on the distance the electricity must travel. Table 1: Transportation costs From City 1 City 2 City 3 To Plant 1 10 11 16 Plant 2 8 14 11 Plant 3 7 10 13 Formulate the above problem as a balanced Transportation problem.Develop a LP model for the transportation problem (cost problem). Solve the LP model to find the optimal solution and the minimum total cost.A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W 1 W 2 W 3 $7.50 $6.75 $6.25 $7.00 $6.50 $8.00 Customer A Customer B Write the objective function and the constraint in equations. Let V;= tons shipped to customer i from warehouse j, and so on. For example, VA1 = tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. b) The objective function for the LP model = Minimize Z = $7.50 + $6.25 + $6.50 (shipping cost to customer A) V + $6.75 + $7.00 + $8.00 (shipping cost to customer B) c) Subject to: Customer A's demand Customer B's demand…
- 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. What is the objective function? Group of answer choices Max Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH Min Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH Min Z = $3AD + $3BE + $5CD + $3CE…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?Please answer it immediately sir Linear Programming The Booboo sawmill in Batangas produces pine and oak boards for manufacturing firms. Each month the sawmill must deliver atleast 5 tons of wood to the manufacturer . It takes the sawmill 3 days to produce a ton of pine and a 2 days to produce a ton of oak and the sawmill can allocate 18 days out of a month for this contract. The sawmill can get enough pine to make atleast 4 tons of wood and enough oak to make atmost 7 tons of wood. Determine the number of tons of pine and oak in order to minimize cost, given that pine has a cost of $3 and oak $6 to produce