Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Source Supply 200 Destination X Y Demand S0 125 125 A B 100 150 Shipping costs are: Destination Source 3 9 Y B 10 6 | (Source B cannot ship to destination Z) A. According to the Northwest Corner method, the initial solution would have a total transportation cost of B. According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of C. According to the minimum cell cost method, the initial solution would have a total transportation cost of

The Hills County, Michigan, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors, A - E, of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assigned to the high school in that sector, there is no need to bus him because he can walk to school. The three schools are located in sectors B, C, and E. The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school: Distance to School Sector School in Sector School in Sector School in Sector B C E A B C D E Total 7 0 4 5 12 5 4 0 4 7 6 12 7 7 0 Number of Students 700 500…

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The HERCULES company's Process Manager should decide the location of his company's facilities. He has come up with 4 options in 4 communities. The table below shows fixed (land purchase costs, taxes, insurance, machinery, building erection costs, etc.) and variable costs (wages, materials, transportation costs, etc.) for each option Community Issues: A B с D Fixed costs (Annual) $ 150,000 $ 300,000 $ 500,000 $ 600,000 Variable costs (per unit of product) $ 62 $ 38 $ 24 $ 30 (a) Calculate the range of output for which each community minimizes its production costs. (b) If the expected demand for the product is 15,000 units per year, in which community would you advise the process manager to locate his company's plant?

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Tommy Hilfiger is currently considering to source certain textile goods, Tommy Jeans, from Mexico. The estimated shipping time from Mexico to the U.S. for each shipment of Tommy Jeans is 4 days and the estimated freight cost of each shipment is $800. On the other hand, the current average shipping time from Vietnam to the U.S. for each shipment of Tommy Jeans is 23 days and the average freight cost is $2300. Even though the shipping time and freight cost seem to be much lower in case of Mexico, Tommy Hilfiger management is concerned about the production cost of each Jeans shipment. The management anticipates that the production cost of each Jeans shipment will be higher in Mexico compared to Vietnam. However, Tommy Hilfiger management has decided that even if the total cost (sum of production cost, freight cost, and holding cost) remain similar to Vietnam, Tommy Hilfiger will still source Jeans from Mexico because of the reduced shipping time, which, in turn, will result in better…

Here is the initial tableau (by the NorthWest method) of a Min transportation problem. 1 2 3 Demand 19 Dual(v) 1 15 9 S1: 11 10 14 0 S2: 0 S3: B 0 B 3 N 15 Demanders 2 8 0 9 12 188 15 9 21 5 N 0 B 0 B 13 10 8 8 20 3 0 20 -4 N -6 N 0 B 17 7 5 4 0 0 1 -14 N -8 N 0 B Supply Dual(u) 0 (188 188 188 188 Using the Loop method fill in the values of the next tableau Each 2x2 matrix is the relevant square in the tableau. 9 (For grading convenience, in bottom right corner of each box use 1 for "B" and 0 for "N") 22 188 188 188 30 -4 2

(2) Find an optimal solution for the following transportation problem. Town To Valley FROM Madison (M) Yonkers (1) Pittsburgh (P) Demand FROM Madison (M) Yonkers Pittsburgh FROM 3.50 Madison (M) Yonkers FROM $8 350 Madison (M) Yonkers (1) Pittsburgh $5 SIS 350 Valley (5) $8 $5 $15 Using the Stepping-Stone method to find an optimal plan. Tol Valley Town Junction (7) $8 Pittsburgh Demand 350 Part (a) Find the new TC= $5 $15 50 350 The above feasible plan is obtained by applying the Northwest Corner Rule (e.g., 300 from M to V, etc.), and its total cost = 350($8) +50($10)+150($12) +250($4)+200($11) +250($14) = $11.800, 150 $8 200 $5 The improvement indices below are determined as follows: Supply row M first, then sows Y and P) MJ: 9-4+12-10-2 400 MB: 6-11+12-10=-3 rv: 5-12+10-8-5 600 PP: 15-14+11-12-10-8-2 PT: 6-14+11-12- PA 11-14+11-4-4 Demand 350 200 the "most negative index" We focus on cell PT (index=-9). Its closed path is: PT to PB to YB to YT, and back to PT. To increase the…

A fruit juice manufacturer has recently begun negotiations with brokers in the areas where it intends to distribute its products. Before finalizing the agreements, however, the manager wants to determine shipping routes and costs. The firm has three plants with the capacities as shown below: Estimate demands in each of the warehouse localities are: PLANT CAPACITY (PIECES PER WEEK) WAREHOUSE 1 2 3 400 800 600 A B C D DEMAND (PIECES PER WEEK) 900 200 400 300 The estimated ship cost per box for the various routes are: ΤΟ FROM A B C D 1 5 7 9 12 2 10 7 2 3 3 8 9 6 4 Row/Column Opportunity Cost Demand Row/Column Cell Total Cost Opportunity Cost Cost of the above Test of unallocated Cells allocation Supply Amount char

2. By using the data below, use a transportation method to : COST in $ Assembly Plant Supply 210 Factory 2 A 8 9 400 10 6 12 8 190 Demand 120 620 60 A. Formulate this linear programming model B. If you are using VAM and NorthWest corner method, which solution is the best and how much is the best total cost ?