Consider the following cost matrix to solve a warehouse location problem to minimize the total setup and cransportation costs. Warehouse sites Cust. Loc. A B 1 100 1000 200 2 1000 100 200 3 500 500 500 Fixed Cost 300 300 X What is the largest integer value for X (fixed cost of cite C) for which the greedy algorithm we have seen in the class gives a solution that is not optimal, regardless of how one break the ties?
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- 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…A manufacturer produces two types of calculator; each requiring material and labour as shown below: Input Scientific Calculator Graphic Calculator Availability Labour (hrs) 4 5 200 Inspection time 2 1 80 Material (cm2) 10 12 600 PROFIT $200 $300 Write the objective function and he constraints Diagram the constraint and identify the feasible region Using the corner point method, identify the production level that meets the objective of maximum profitConsider 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
- 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 10We have three Suppliers and four Demanders. the Suppliers have inventory of 61 , 49, 29 respectively, and the Demanders require 54, 37, 4, 44 respectively. Shipping costs from S1 to D1, D2, D3 , D4 are 103, 30, 68, 54from S2 to D1, D2, D3 , D4 are 16, 95, 84, 35from S3 to D1, D2, D3 , D4 are 40, 44, 46, 101. Check that this is a balanced transportation problem. Find the optimal mimimal shipping cost: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
- 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 followingg linear programming problem: Max 3A + 3Bst. 2A + 4B ≤ 12 6A + 4B ≤ 24 A, B ≥ 0 The point (0.0,0.0) is: a. infeasible. b. is one of the extreme points. c. the optimal solution. d. unboundedConsider 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.
- Consider 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?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 problemA company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requiremnet are 180, 120 and 150 units, respectively. Unit shipping costs (in rupess) are as follows: W1 W2 W3 Supply F1 16 20 12 200 F2 14 8 18 160 F3 26 24 16 90 Demand 180 120 150 450 Determine the optimal distribution for this company to minimize total shipping cost.