week 10

MAT540 Homework Week 10 Page 1 of 2

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page1image5848

From

To (cost)

Supply

1

2

3

A

$5

$4

$3

130

B

2

3

5

70

C

4

8

7

100

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Demand

80

page1image34536 page1image34960

110

60

 
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From

To (cost)

page1image43016

Supply

page1image44280

1

2

page1image46856

page1image47584

3

page1image48640

A

$5

$ 12

$2

130

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B

2

page1image55984

9

5

70

page1image59272

C

4

page1image61832

24

7

100

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Demand

80

page1image68496

page1image68800

110

60

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Solve it by using the computer.

3. World Foods, Inc., imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver the products to Norfolk, New York and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are then distributed to specialty foods stores and sold through catalogs. The shipping costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are provided in the following table:

The transportation costs ($/1,000 lb.) from each U.S. city of the three distribution centers and the demands (1,000 lb.) at the distribution centers are as follows:

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From

To (cost)

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Supply

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4. Norfolk

5. New York

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6. Savannah

1. Hamburg

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$420

$390

$610

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55

2. Marseilles

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510

590

470

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78

3. Liverpool

450

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360

480

37

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Warehouse

Distribution Center

 

MAT540 Homework Week 10 Page 2 of 2

Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs.

4. The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table:

 

7. Dallas

8. St. Louis

9. Chicago

4. Norfolk

$ 75

$ 63

$ 81

5. New York

125

110

95

6. Savannah

68

82

95

Demand

60

45

50

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Region (days)

Sales- person

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A

B

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C

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D

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E

1

page2image43312

17

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10

page2image46888

15

page2image48400

16

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20

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2

12

9

16

9

14

3

page2image57328

11

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16

page2image60904

14

page2image62416

15

page2image64080

12

page2image65480

4

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14

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10

10

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18

page2image71424

17

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5

13

12

9

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15

11

Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time. 

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