For the network shown below, the arc capacity from node i to node j is the number nearest node i along the arc between these nodes. formulate the maximum flow as a linear programming problem.
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)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?At the end of a cycle of schedules, a trucking firm has a surplus of one vehicle each in cities A, B, C, D, E, and F and a deficit of one vehicle each in cities 1, 2, 3, 4, 5, and 6. The distances between cities with a surplus and the cities with a deficit are shown below. Find an assignment of surplus vehicles to deficit cities that will result in a minimum total distance. What is the total distance? -Solve the following transportation models using Excel Solver. -Find the optimal solution for the transportation problem having the cost and requirement tablebelow.
- Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Minimize z = x + y Subject to 4x + y ≥ 50 x + 4y ≥ 50 x ≤ 23 y ≤ 23 Minimum value is z = at(x, y) = ( , )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:…Transeast Airlines flies planes on the following route:L.A.–Houston–N.Y.–Miami–L.A. The length (in miles) ofeach segment of this trip is as follows: L.A.–Houston, 1,500miles; Houston–N.Y., 1,700 miles; N.Y.–Miami, 1,300miles; Miami–L.A., 2,700 miles. At each stop, the planemay purchase up to 10,000 gallons of fuel. The price of fuelat each city is as follows: L.A., 88¢; Houston, 15¢; N.Y.,$1.05; Miami, 95¢. The plane’s fuel tank can hold at most12,000 gallons. To allow for the possibility of circling overa landing site, we require that the ending fuel level for eachleg of the flight be at least 600 gallons. The number ofgallons used per mile on each leg of the flight is1 (average fuel level on leg of flight/2,000)Review Problems 123To simplify matters, assume that the average fuel level onany leg of the flight isFormulate an LP that can be used to minimize the fuel costincurred in completing the schedule
- A beer distributor needs to plan how to make deliveries from its warehouse (node 1) to a supermarket (node 7), as shown in the network below. A graph with 7 nodes and 9 arcs is shown. Node 1 is connected to node 2 by arc of value 3, to node 5 by arc of value 3, and to node 6 by arc of value 11. Node 2 is connected to node 3 by arc of value 4. Node 3 is connected to node 2 by arc of value 4 and to node 4 by arc of value 7. Node 4 is connected to node 3 by arc of value 7, to node 6 by arc of value 5, and to node 7 by arc of value 6. Node 5 is connected to node 6 by arc of value 7. Node 6 is connected to node 4 by arc of value 5, to node 5 by arc of value 7, and to node 7 by arc of value 3. Develop the LP formulation for finding the shortest route from the warehouse to the supermarket. (Let xij represent the flow from node i to node j.) Min s.t.Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows Node 7…Explain all the steps when implementing the Branch and Bound method for the following optimization problem: Max 15*x1+12*x2+4*x3+2*x4 s.t. 8*x1+5*x2+3*x3+2*x4 <=10 3*x1+2*x3<=4 x1, x2, x3, x4 binaryThe following diagram represents a flow network. Each edge is labeled with its capacity, the maximum amount of stuff that it can carry. a. Formulate an algebraic model for this problem as a maximum flow problem. b. Develop a spreadsheet model and solve this problem. What is the optimal flow plan for this network? What is the optimal flow through the network?
- 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-allocationA 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…