MAT540 Week 10 Homework MAT 540 Week 10 Homework MAT/540 Week 10 Homework

These problems can be done by using QM.

Chapter 6 1. Consider the following transportation problem:

                                                           To (cost)    

From                                     1                 2                  3                      Supply

A                                          $ 5               $ 4               $3                          130

B                                             2                  3                  5                            70

C                                             4                  8                   7                          100

Demand                             80               110                60

Formulate this problem as a linear programming model and solve it by using the computer. Write out your solution as well.

2. Consider the following transportation problem: (Do not do this problem)

To (cost)

From                                     1             2              3                              Supply

A                                          $ 5         $ 12           $ 2                                130

B                                            2                9              5                                    70

C                                            4              24              7                                  100

Demand                            80            110           60

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:

                                                                                  To (cost)

From                     4. Norfolk            5. New York                        6. Savannah                        Supply

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. Formulate this problem as a linear programming model by using the assignment model and solve it by using the computer. Write out your solution as well.

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:

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.  Formulate this problem as a linear programming model and solve it by using the computer. Write out your solution as well.