An initial solution to a transportation problem is given below. a. Use Northwest, MCM and VAM to determine the initial solution b. Use the stepping stone method to determine if the solution is optimal in VAM. c. Generate the optimal solution based on (b)
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- 3. Two poultry farms supply companies with chicken feeds. The unit costs of shipping from the farms to the companies are given in the table below. The farm's goal is to minimize the cost of meeting customers' demands. a) Generate a mathematical model for finding the least cost way of shipping chicken feeds from the farms to the companies.(b) if the demand of company number 2 increased by 3 units. By how much would the costs increase? Show your solution. (c). Solve the total cost using the solver add-in in excel. From Company 1 Company 2 Company 3 Supply Farm A 55 65 80 35 Farm B 10 15 25 50 Demand 10 10 10Consider the following linear program: Max 3A + 3B S.t. 2A + 4B < 12 6A + 4B < 24 A, B > 0 Find the Optimal Solution using the graphical solution procedure If the objective function is changed to 2A + 6B, what will the optimal solution be? How many extreme points are there? What are the values of A and B at each extreme point?Consider the transportation table below. REQUIREDa. Define the decision variablesb. Write a linear programming model for this problem.c. Use the Northwest-Corner Method, the Least-Cost Method and the VAM to getthe starting feasible solution.d. Find the optimal solution using the transportation algorithm discussed in class by considering the least optimal of the objective function computed in (c).e. Formulate a network model to illustrate the optimal solution
- Two plants supply three customers with medical supplies. The unit costs of shipping from the plants to the customers, along with the supplies and demands, are given in Table below. The company’s goal is to minimize the cost of meeting customers’ demands. From To Customer 1 Customer 2 Customer 3 Supply Plant 1 55 65 80 35 Plant 2 10 15 25 50 Demand 10 10 10 Formulate a linear programming (LP) model for this problem. Use solver to find the optimal transportation rule As a management science student, the MD of the company seeks your expert advice on ways in which to determine the optimal transportation rule. Advise the MD, providing detailed explanation using your answer obtain in (b). Write your answer in a form of a report to the MD.Modify the warehouse location model as suggested inModeling Issue 2. Specifically, assume that the samefour customers have the same annual shipments, butnow, there are only two possible warehouse locations,each with distances to the various customers. (Thesedistances, along with other inputs, are in the fileP07_27.xlsx.) The company can build either or bothof these warehouses. The cost to build a warehouseis $50,000. (You can assume that this cost has beenannualized. That is, the company incurs a buildingcost that is equivalent to $50,000 per year.) If onlyone warehouse is built, it will ship to all customers. However, if both warehouses are built, then the com-pany must decide which warehouse will ship to each customer. There is a traveling cost of $1 per mile.a. Develop an appropriate model to minimize totalannual cost, and then use Solver to optimize it.Is this model an NLP or an IP model (or both)?b. Use SolverTable with a single input, the traveling costper mile, to see how large…General 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 costDefine the decision variablesand Write a linear programming model for this problem. B. Use the Northwest-Corner Method, the Least-Cost Method and the VAM to getthe starting feasible solution.ThenFind the optimal solution using the transportation algorithm discussed in class by considering the least optimal of the objective function computed. 3.C.Formulate a network model to illustrate the optimal solution.consider the following network representation of a transportation problem:(The image provided) The supplies, demands, and transportation costs per unit are shown on the network. The optimal (cost minimizing) distribution plan is given below. Des Moines Kansas City St.Louis Supply Jefferson City 20 0 10 30 Omaha 10 10 0 20 Demand 30 10 10 Total Cost: $530. Find an alternative optimal solution for the above problem. If required, round your answer to nearest whole number and if your answer is zero enter “0” Des Moines Kansas City St.Louis Jefferson City Omaha Total Cost: $ is?
- Consider the followingg linear programming problem: Max 3A + 3Bst. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0 The point (4.0,0.0) is: a. unbounded. b. is one of the extreme points. c. the optimal solution. d. infeasible.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 248Consider the followingg linear programming problem: Max 3A + 3Bst. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0 The point (0.0,6.0) is: a. the optimal solution. b. is one of the extreme points. c. infeasible. d. unbounded.