Most of the other types of network flow problems can be viewed as simple variations of the transshipment problem. True False
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- 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 160The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of 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 lowest cost option to travel from city A to city M. Which type of network optimization problem is used to solve this problem? Multiple Choice: Minimum Flow Problem Average-Cost Flow problem Maximum Flow Problem Shortest Path Problem Maximum-Cost Flow problemThe Hamilton County Local Government has eight sectors which need fire protection. Adequate Fire protection can be provided in each sector either by building a fire station in that sector, or by building a fire station in another sector which is no more than a 12-minute drive away. The time to drive between the centers of each pair of sectors is given in the following table. (Because of one-way streets and left turns the times are not symmetric.) The cost to build a fire station is the same in each sector. Formulate an integer programming model to choose which sectors should have their own fire station. Solve the model by using Excel Solver.
- Sunco Oil produces oil at two wells. Well 1 canproduce up to 150,000 barrels per day, and well 2 canproduce up to 200,000 barrels per day. It is possible toship oil directly from the wells to Sunco’s customersin Los Angeles and New York. Alternatively,Sunco could transport oil to the ports of Mobile andGalveston and then ship it by tanker to New Yorkor Los Angeles. Los Angeles requires 160,000 barrelsper day, and New York requires 140,000 barrels perday. The costs of shipping 1000 barrels betweenvarious locations are shown in the file P05_55.xlsx,where a blank indicates shipments that are not allowed.Determine how to minimize the transport costs inmeeting the oil demands of Los Angeles and New York.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 (W1) 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 Customer A $7.50 $6.25 $6.50 Customer B $6.75 $7.00 $8.00 Write the objective function and the constraint in equations. Let Vij= 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. Part 2 b) The objective function for the LP model =Consider the transportation problem having the following data: c) write the algebraic formulation of this problem.
- A transportation problem involves the following costs, supply, and demand: Solve this problem by using the computer.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?Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The costs of shipping between the respective plants is shown in the table below: Grand Rapids Blue Ridge Sunset Ohio Valley 50 40 100 Lakeview 60 50 75 Implement the LP model in Solver and obtain the optimal shipping plan. What is the optimized cost?
- Luminous lamps have three factories - F1, F2, and F3 with production capacity 30, 50, and 20 units per week respectively. These units are to be shipped to four warehouses W1, W2, W3, and W4 with requirements of 20, 40, 30, and 10 units per week respectively. The transportation costs (in Rs.) per unit between factories and warehouses are given below. Find an initial basic feasible solution.The Easy Time Grocery chain operates in major metropolitan areas on the East Coast. The stores have a “no-frills” approach, with low overhead and high volume. They generally buy their stock in volume at low prices. However, in some cases they actually buy stock at stores in other areas and ship it in. They can do this because of high prices in the cities they operate in compared with costs in other locations. One example is baby food. Easy Time purchases baby food at stores in Albany, Binghamton, Claremont, Dover, and Edison and then trucks it to six stores in and around New York City. The stores in the outlying areas know what Easy Time is up to, so they limit the number of cases of baby food Easy Time can purchase. The following table shows the profit Easy Time makes per case of baby food, based on where the chain purchases it and at which store it is sold, plus the available baby food per week at purchase locations and the shelf space available at each Easy Time store per week:…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…