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MAT540

 

Week 10 Homework

 

Chapter 6

 

  1. Consider the following transportation problem:

 

From

To (cost)

Supply

1

2

3

A

$  6

  $  9

$100

130

B

12

3

5

70

C

4

8

11

100

Demand

80

110

60

 

 

 

 

Formulate this problem as a linear programming model and solve it by using the computer.

 

 

 

  1. Consider the following transportation problem:

 

From

To (cost)

Supply

1

2

3

A

$  6

$  9

$  7

130

B

12

3

5

70

C

4

8

11

100

Demand

80

110

60

 

 

 

 

Solve it by using the computer.

 

  1. 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:

 

From

To (cost)

Supply

4. Norfolk

5. New York

6. Savannah

1. Hamburg

$420

$390

$610

55

2. Marseilles

510

590

470

78

3. Liverpool

450

360

480

37

 


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:

 

Warehouse

Distribution Center

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

 


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

 

 

 

  1. 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:

 

 

Region (days)

Sales-person

A

B

C

D

E

1

17

10

15

16

20

2

12

9

16

9

14

3

11

16

14

15

12

4

14

10

10

18

17

5

13

12

9

15

11

 

 

 

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