Determine the optimal shipments between the european ports

Question

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	1	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
Demand	110	140	100

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 (S/I,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	320	280	555	75
2. Marseilles	410	470	365	85
3. Liverpool	550	355	525	40

The transportation costs (S11000 lb.) from each U.S. city of the three distribution centers and the demands (1000 lb.) at the distribution centers are as follows:

Warehouse	To (Cost)
	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.

Answer 1

By using the table and information provided in the assignment above, consider it carefully and on the basis of that information, provide solution to the given problem by illustrating the concepts used. The Omega Pharmaceutical firm consists of five salespersons, which the firm wishes to allocate to five sales regions. Given their different previous contacts, the sales persons are capable to cover the areas in diverse amounts of time. The amount of time (days) needed by each salesperson to cover each city is illustrated in the table above. Which salesperson must be allocated to each area to minimize the total time? Recognize the optimal assignments and calculate the total minimum time.