Consider the following transportation problem

| August 30, 2017

Question
MAT540 Homework
Week 10
Page 1 of 2
MAT540
Week 10 Homework
Chapter 6
1.

Consider the following transportation problem:

From

To (Cost)

Supply

1

2

3

A

6

5

5

150

B

11

8

9

85

C

4

10

7

125

Demand

70

100

80

Formulate this problem as a linear programming model and solve it by the using the computer.
2.

Consider the following transportation problem:

From

To (Cost)

Supply

1

2

3

A

8

14

8

120

B

6

17

7

80

C

9

24

10

150

110

140

100

Demand

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:

MAT540 Homework
Week 10
Page 2 of 2
To (Cost)

From

4.

Norfolk

5.

Supply

New York

6.

Savannah

1. Hamburg

320

280

555

75

2. Marseilles

410

470

365

85

3. Liverpool

550

355

525

40

The transportation costs ($/1000 lb.) from each U.S. city of the three distribution centers and the
demands (1000 lb.) at the distribution centers are as follows:
Distribution Center

Warehouse
7. Dallas

8. St. Louis

9. Chicago

4. Norfolk

80

78

85

5. New York

100

120

95

6. Savannah

65

75

90

Demand

85

70

65

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 sales persons 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:

Salesperson

Region (days)
A

B

C

D

E

1

20

10

12

10

22

2

14

10

18

11

15

3

12

13

19

11

14

4

16

12

14

22

16

5

12

15

19

26

23

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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