2c. Determine the maximum flow from node 1 to node 5 in the network shown below (numbers on arcs denote flow capacities). 15 10 30 2 30 40 10 15 3 20 20 5
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- Q.) Given the following network, with the indicated flow capacities along each branch, determine the maximum flow from source rode 1 to destination node 6 and the flow along each branch: 15 12 20 0 14 11Describe in your own words assumptions of Maximal Flow Problem by indicating any differences with the assumptions of Transshipment Problem.Suppose as many as 300 cars per hour can travelbetween any two of the cities 1, 2, 3, and 4. Set up amaximum-flow problem that can be used to determine howmany cars can be sent in the next two hours from city 1 tocity 4. (Hint: Have portions of the network represent t 0,t 1, and t 2.)
- A company with a network of 10 pipelines transports mango juice according to the details shown in Table 1. Determine the maximum flow per hour. 1. Table/Jadual 1 Сарacity Node Node (m3/h) 140 100 120 100 120 80 110 100 100 100 Reverse Capacity |(m³/h) 60 20 40 40 40 20 30 40 60 60 Start End Pipeline 1 2 3 4 1 1 1 2 3 4 6 6 7 3 7 7 8 8 10Problem 6-33 For the following highway network system, determine the maximal flow in vehicles per hour: 3 Maximal flow 2 2 5 2 Vehicle flow capacity: 5000 vehicles per hour vehicles per hour. The highway commission is considering adding highway section 3-4 to permit a flow of 2,000 vehicles per hour or, at an additional cost, a flow of 3,000 vehicles per hour. What is your recommendation for the 3-4 arc of the network? Recommended capacity ▼ vehicles per hour.City Cab Company identified 10 primary pickup and drop locations for cab riders in New York City. In an effort to minimize travel time and improve customer service and the utilization of the company's fleet of cabs, management would like the cab drivers to take the quickest route between locations whenever possible. The travel times in minutes are shown on the arcs of the network. Note that there are two one-way streets and that the direction is shown by the arrows. 1 I 13 10 15 10 2 5 3 2 4 4 5 15 3 5 6 12 2 7 5 8 4 7 9 Using the above network of roads and streets, what is the quickest route a driver beginning at location 1 should take to reach location 10? path = 1, 10
- eBook Problem 10-31 A long-distance telephone company uses a fiber-optic network to transmit phone calls and other information between locations. Calls are carried through cable lines and switching nodes. A portion of the company's transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can be transmitted over that branch of the network. To keep up with the volume of information transmitted between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city located at node 1 to a oty located at node 7. 3 Maximum number of messages -Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram is given in the figure below shows the possible routes and distances from the carpet plant in Valparaiso to the various warehouses or retail outlets. 12 11 13 Hi 6 15 20 10 M На(1) Find an optimal assignment of trucks to routes to minimize the total cost (using the Hungarian Method). B C 6 12 15 10 11 7 16 9 Truck / Route 1 2 3 4 Step la: Row subtraction (show your steps, e.g., see cell 1A) Truck / Route B 1 2 3 4 A 10 11 9 14 Step 1b: Column subtraction. Truck / Route 1 2 3 4 A 10-6=4 = = = = = B = с = C Step 2: Testing for optimal solution (show your lines covering the zero entries). What is the minimum number of lines required to cover all zeros? D 8 14 10 13 D = = D =
- Consider the following network representation of a transportation problem. Let Min 40 s.t. 35 Supplies From Jefferson City From Omaha To Des Moines Jefferson City To Kansas City Omaha To St. Louis 14 9 8 X11 = amount shipped from Jefferson City to Des Moines X12 = amount shipped from Jefferson City to Kansas City X13 = amount shipped from Jefferson City to St. Louis X21 amount shipped from Omaha to Des Moines X22 = amount shipped from Omaha to Kansas City X23 = amount shipped from Omaha to St. Louis 8 11 24 The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your model. Des Moines Kansas City St. Louis 25 10 40 Demandsplease do it in excel BETTER PRODUCTS COMPANY has decided to start manufacturing four new products in three plants that currently have excess production capacity. The products require comparable production effort per unit, so the available production capacity in the plants is measured by the number of units of any product that can be manufactured per day. a)Formulate this problem as a transportation problem by constructing the appropriate parameter table. Note:One image is of the data and the other image is option 1 to solve the exercise.Maxie is leaving the Goucher Basketball jersey making business and is closing three of her factories. She would like to reassign all 235 of her best workers to Bianca's remaining factories. Closing Plant: No. of Workers to Transfer 1 60 2 105 3 70 Total: 235 However, demand for skilled labor in the Goucher basketball jersey making market has decreased. Bianca has three open plants that have openings, but not enough for all 235 employees looking to be transferred. The below table summarizes Bianca's current needs: Open Plant: No. of Open Positions A 45 B 90 C 35 Total: 170 Each worker who fills an open position on the assembly line will increase the number of Goucher basketball jerseys produced per day at each plant as shown in the following table: To: From: A B C 1 5 8 6 2 10 9 12 3 7 6 10 To maximize product output, how many workers should be assigned from Plant 1 to.. Plant A: Plant B: Plant C: from Plant 2 to.. Plant A: Plant B: Plant C: from Plant 3 to.. Plant A: Plant B: Plant C:…