1.         A company has factories at F1, F2 and F3 which supply warehouses at W1, W2 and W3 and W4. Weekly factory capacities are 100, 125 and 75 units. Weekly warehouse requirements are 70, 90, 80 and 60 units respectively. Units shipping cost (in rupees) are as follows :

 Factory Warehouse W1 W2 W3 W4 SUPPLY F1 6 5 1 3 100 F2 4 8 7 2 125 F3 6 3 9 5 75 Demand 70 90 80 60

Determine the optimum distribution for the company to minimize the shipping cost. Use NWCR to obtain Initial Solution

2.      Solve the following transportation problem for minimum cost by taking initial feasible solution by North West corner rule and Vogel’s approximation method. The entries in the matrix indicate the cost in rupees of transporting a unit from a particular source to a particular destination.

 Origin Destination Supply 1 2 3 4 1 10 8 11 7 20 2 9 12 14 6 40 3 8 9 12 10 35 Requirement 16 18 31 30 95

3.         A company is spending ` 12000 /- on transportation of finished goods from 3 plants to four distribution centers every month. The supply and demand for finished goods every month with unit cost of transportation are given in the following table

 Plants / Distribution center D1 D2 D3 D4 Monthly Supply F1 20 30 50 15 7 F2 70 35 40 60 10 F3 40 12 60 25 18 Monthly demand 5 8 7 15
• Find the optimal solution to give minimum cost schedule to transport finished goods to market
• What can be the maximum saving every month by optimal scheduling?

4.        The following table gives the data regarding the transportation timings from 4 different origins to 4 different destinations. The available material to be transported from 4 origins are 5,7,8,10 thousand tones, whereas the intake capacity of different destinations are 10,5,10,5 thousand tones respectively. Using appropriate method, find the basic feasible solution to this transportation problem and also obtain the optimum solution so as to minimize transportation timings:

 Destination Dl D2 D3 D4 Origin O1 6 7 3 4 O2 7 9 1 2 O3 6 5 16 7 O4 18 9 10 2

5.         Four warehouses with capacities of 85, 35, 50 and 45 tons were receiving the materials from 3 factories with the supply capacity as 70, 55 and 90 tons on regular basis. The transportation cost per ton from factories to warehouses are given in the following table:

 Factory Warehouse 1 2 3 4 I 6 1 9 3 II 11 5 2 8 III 10 12 4 7

A feasible solution states that from Factory I, 25 tons have to be transported to warehouse 3 and 45 tons to warehouse 4. Similarly 30 tons and 25 tons were transported from Factory II to Warehouse1 and warehouse 3 respectively. However, from Factory III, 55 tons and 35 tons were transported to warehouse 1 and warehouse 2 respectively. Is this transportation schedule optimum? If not modify it and obtain optimum solution and optimal cost.

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