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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.