23. Find the shortest route from node 1 to node 7 in the network shown. 18 6 7
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- 15. Paryente Times, Inc, a publisher headquartered in Manila, wants to assign three recently hired college graduates, Marvin, Marlon, and Kevin to regional sales districts in Ceu, loil nd Davao. But the firm also has an opening in Makati and would send one of the thee here i it were more economical than move to Cebu, loilo, or Davao. Itwil cost P1,00 o relocate Marvin to Makati, P800 to relocate Marlon there, and P1,500 to move Kevin. What is the optimal assignment of personnel to offices? Cebu loilo Davao Marvin P800 P1,100 P1,200 Marlon P500 P1,600 P1,300 Kevin P500 P1,000 P2,300QUESTION 21. Mr. Jack is in the process of expanding his manufacturing business. He decided to opena plant in the coming year. He has four locations in mind. The costs information for these locations is in the following table.Locations A B C DFixed Costs 60,000 80,000 100,000 130,000Variable Costs/unit 30 20 15 10a.i. Write an equation to represent the total costs for each location. ii. Draw the total costs lines for each location on the same axes. (Use output rangesof 200, 400, 600, 800 etc. and intervals of $50,000 on the Y axis.iii. Over what range of output is location A the most preferred location?iv. Over what range of output is location B the most preferred location?v. Over what range of output is location C the most preferred location?1. Given 6 customers and the costs (distances) between them, find the best route/scheduling using the savings method. Figure 1. Customers' locations (One of the customers is chosen as 0 for your convenience) 3 O 5 Table 1. The costs (distances) between customers Cu 0 1 0 1 2 3 4 5 10 6 13 17 5 10 5 8 6 8 6 5 7 11 9 2 13 8 7 10 16 3 17 6 11 10 10 5 8 9 16 10 1 5
- Facility Location. A paper products manufacturer has enough capital to build and manage some additional manufacturing plants in the United States in order to meet increased demand in three cities: New York City, NY; Los Angeles, CA; and Topeka, KS. The company is considering building in Denver, CO; Seattle, WA; and St. Louis, MO. Max Operating Capacity 400 tons/day 700 tons/day Denver Seattle $10/ton $17/tor $5/ton $11/ton.... $18/ton.... $28/ton Los Angeles Topeka New York City Figure 1: Graphical representation of the given data = • The cost fi of building plants in these cities is fi $10,000,000 in Seattle. Unmet Demand 300 tons/day 100 tons/day 500 tons/day • Due to geographic constraints, plants in Denver and Seattle would have a maximum operating capacity kį of 400 tons/day and 700 tons/day respectively. $5,000,000 in Denver and f2 = • The cost cij per ton of transporting paper from city i to city j is outlined in Figure 1. • The unmet demand d, for Los Angeles, Topeka, and New…Define line extension.PROBLEM 2 From the next network, answer the questions. 8 A D 9. 6. G S 17 15 8 24 2 2 20 8 F H 11 22 14 5 3 18 4 8 B E U 5 a) Find the maximum flow from points A and B to point U, using the augmented path algorithm. b) Model this maximum flow problem according to minimum cost flow modeling (minimization) c) Model this_problem in maximization.
- 23. Find the shortest route from node 1 to node 7 in the network shown. 5 4 6. 9. 3 18 3 3Question 3 i. Sap Manufacturing, a manufacturing company that manufactures football jerseys and located in Port Antonio, Jamaica, is preparing to build a new plant. J's is considering three potential locations that are suitable for the construction of the plant. The fixed and variable costs for the three alternative locations are presented in the table below. Table 4 Costs A B C Fixed Costs ($) 700,000 1, 000,000 1,100,000 Variable ($ per unit) 28 20 18 a. Identify the range over which each alternative (A, B and C) is best.Q Let us assume that a new medical facility, Health-care, is to be located in XYZ city. The location factors, factor rating and scores for two potential sites are shown in the following table. Which is the best location based on factor rating method? Sr Location factor Factor Rating Rating Location 1 Location 2 1 Facility utilization 10 5 4 2 Total patient per month 8 4 2 3 Average time per emergency trip 5 4 5 4 Land and construction costs 6 3 4 5 Employee preferences 7 4 4 6 Operations Facility 8 4 3
- The National Post Company has established various truck routes around Leb- anon over which it ships parcels. The holiday season is approaching which means a dramatic increase in the number of packages that will be sent. The company wants to know the maximum flow of packages it can accommodate, in tons, from station 1 to station 7. The network of routes and the flow capac- ities, in tons of packages per day, along each route are shown in the following network: 6 5 1 2 2 6 3 3 7 4 2 4 6 4 2 3 5 9 2 6 4 0 0 0 7 a. Determine the maximum tonnage of packages that can be transported per day from station 1 to station 7, HAND b. Indicate the flow along each branch.F Source 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. 1 4 24 3 33 4 4 54 69 7 Sink F Iteration Augmenting path 1 2 3 C*Question 27 Finally, passenger rail service comes to Ohio, connecting the six major cities. Here is the planned network with the daily passenger capacity on each segment for one way travel between Cincinnati and Cleveland: Cincinatti (A) to Dayton (B) 500 Dayton (B) to Toledo (C) 200 Dayton (B) to Columbus (D) 250 Columbus (D) to Toledo (C) 100 Columbus (D) to Akron (E) 400 Toledo (C) to Cleveland (F). 250 Akron (E) to Cleveland (F) 450 Formulate a model to maximize flow of the passenger traffic from Cincinnati to Cleveland. What is the proper Objective Function for this problem? O MAX 500XAB + 200Xgc + 250XBD + 100Xpc + 400XpE + 250XCF + 450XEF O MAX A + B+C+D+E+ F O MAX XAF MAX XFA