Given the following information, what is the shortest distance using the minimum spanning tree technique? Branch Distance 1 to 2 32 1 to 7 21 1 to 8 22 2 to 3 33 2 to 7 23 3 to 4 27 4 to 5 30 4 to 7 20 5 to 6 29 6 to 7 22 6 to 8 19 O 161 159 O 158 162 160 O O O
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- We illustrated how a machine replacement problem can be modeled as a shortest path problem. This is probably not the approach most people would think of when they first see a machine replacement problem. In fact, most people would probably never think in terms of a network. How would you model the problem? Does your approach result in an LP model?The network below shows the flows possible between pairs of six locations. A graph with 6 nodes and 13 directed arcs is shown. Node 1 is connected to node 2 by arc of value 17, to node 3 by arc of value 19, and to node 5 by arc of value 9. Node 2 is connected to node 3 by arc of value 8 and to node 4 by arc of value 14. Node 3 is connected to node 2 by arc of value 5, to node 4 by arc of value 9, to node 5 by arc of value 7, and to node 6 by arc of value 24. Node 4 is connected to node 3 by arc of value 9 and to node 6 by arc of value 13. Node 5 is connected to node 3 by arc of value 7 and to node 6 by arc of value 11. Node 6 has no directed arcs directed to other nodes. Formulate an LP to find the maximal flow possible from node 1 to node 6. (Let xij represent the flow from node i to node j. Enter your maximum flows as a comma-separated list of inequalities.) Max s.t.Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows…The figure below shows the nodes (A−I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I. Which nodes are the sink and source for this problem? Multiple Choice: Node A is the source, Node I is the sink. Node A is the sink, Node B is the source. Node A is the sink, Node I is the source. Node B is the sink, Node I is the source. Node B is the source, Node I is the sink.
- The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69 (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations. Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…Instructions: Solve using Excel Solver. Create the linear programming model and get the optimal solution to the problem. (Follow the steps and format in the photo below) 1. A company manufactures two products X1 and X2 on three machines A, B, and C. X1 requires 1 hour on machine A and 1hour on machine B and yields a revenue of Php 30. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of PhP 50. In the coming planning period the available time of three machines A, B, and C are 2000 hours, 1500 hours and 600 hours respectively. Find the optimal product mix.A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs Customer per unit Plant 1 2 3 A $ 25 $ 35 $ 15 B $ 20 $ 30 $ 40 C $ 40 $ 35 $ 20 D $ 15 $ 20 $ 25 The firm needs to satisfy all demand each day, but would like to minimize the total costs. The firm’s problem falls within which classification? Multiple Choice Cost-benefit-trade-off Assignment problems Transshipment problems Transportation problems Resource-allocation
- A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below: Shipping Costs Customer per unit Plant 1 2 3 A $ 25 $ 35 $ 15 B $ 20 $ 30 $ 40 C $ 40 $ 35 $ 20 D $ 15 $ 20 $ 25 The firm needs to satisfy all demand each day, but would like to minimize the total costs. Which of the following constraints is unnecessary for this problem (xi,j is the number of widgets shipped from factory i to customer j)? A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced…The figure below shows the possible routes from city A to city J as well as the time (in minutes) required for a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the quickest option to travel from city A to city J. What is the shortest time possible to travel from node F to node J. Multiple Choice: 200 140 110 180 160Consider the following tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task. There exists unlimited demand unless stated otherwise. Time to Complete Task (seconds): Task 1: 30 Task 2: 25 Task 3: 15 Task 4: 20 Task 5: 15 Task 6: 20 Task 7: 50 Task 8: 15 Task 9: 20 Task 10: 25 Task 11: 15 Task 12: 20 The current conveyor-paced assembly-line configuration assigns the workers in the following way: • Worker 1: Tasks 1, 2, 3 • Worker 2: Tasks 4, 5, 6 • Worker 3: Tasks 7, 8, 9 • Worker 4: Tasks 10, 11, 12 What is the direct labor content (in seconds per unit)?
- The logistic company headquartered in New York wants to expand its business in Chicago, Texas, and Las Vegas. They will place 3 branch heads (A, B a, nd C) from several branch offices owned by the company to set-up offices and run operations in these 3 locations. Below are the costs for allocating the 3 branch heads to each location: Chicago Texas Las Vegas A $8,000,000 $11,000,000 $12,000,000 B $5,000,000 $15,000,000 $13,000,000 C $5,000,000 $10,000,000 $23,000,000 a. Create a table using the assignment method.b. Based on the results of your calculations, what advice can you give to the leader of the company for the most optimum companylocation placement of each of the above branch heads? Explain why?c. What is the total optimum cost that must be incurred by the company to allocate all company branch offices?Can you please solve this Q using Solver for the case of High capacity. please make all the steps clearThe Sav-Us Rental Car Agency has six lots in Nashville, and it wants to have a certain number of cars available at each lot at the beginning of each day for local rental. The agency would like a model it could quickly solve at the end of each day that would tell it how to redistribute the cars among the six lots in the minimum total time. The times required to travel between the six lots are as follows: To (min.) From 1 2 3 4 5 6 1 12 17 18 10 20 2 14 10 19 16 15 3 14 10 12 8 9 4 8 16 14 12 15 5 11 21 16 18 10 6 24 12 9 17 15 The agency would like the following number of cars at each lot at the end of the day. Also, shown is the number of available cars at each lot at the end of a particular day. Determine the optimal reallocation of rental cars. Lot (cars) Cars 1 2 3 4 5 6 Available 37 20 14 26 40 28…