Question

A soft drink manufacturing company has 3 factories set up one in each of the three cities - Orland, Tampa, and Port St. Lucie and it supplies the produced soft drink bottles to 3 warehouses located in the city of Miami. The associated per-unit transportation cost table is provided below:

Transportation Costs ($)
Factories/Warehouse (W)
W1
W2
W3
Orlando
4
3
7
Tampa
7
6
4
Port St. Lucie
3
6
6
The factory at Orlando has a capacity of 15,000 units. The factory at Tampa has a capacity of 18,000 units. The factory at Port St. Lucie has a capacity of 8,000 units.
The requirements of the warehouses are:
Warehouse
Requirement (Bottles)
W1
18,000
W2
12,000
W3
5,000
How many decision variables do you have in this problem?

Answer 1

In this problem, the decision variables represent the number of units (bottles) transported from each factory to each warehouse. Since there are 3 factories and 3 warehouses, there will be a total of 3 x 3 = 9 decision variables representing the transportation quantities between each factory and warehouse combination.