The Imperial Flack Jacket Company currently ships all products out of two factories (A and B) to two government warehouses. Because of increasing demand, another factory will have to be built. The company has two possible locations in mind (C or D) and is currently trying to choose between them using the Linear Programming (LP) transportation method. Data on monthly shipping and receiving volumes and per‑unit shipping costs are: Factory Warehouse 1 Warehouse 2 Production capacity Existing A $2.80 $3.45 2,000 Existing B $2.50 $4.10 3,500 Proposed C $3.25 $3.10 4,000 Proposed D $2.95 $3.55 4,000 Min. Demand 5,000 4,000 How many decision variables are involved in either LP formulation (i.e., with using either proposed location C or D excluding the non-negativity constraint)?

There will be 2 LP formulations as given with one using location C along with A and B and other using location D along with A and B. The LP formulation and solution which gives the minimum total cost while meeting all the constraints will be finally chosen.

In either LP formulation we need to decide on how many units of products are sent from each of the 3 locations - A, B and C or D to the 2 warehouses - 1 and 2. Thus there will be 3 locations and 2 warehouses in each of the LP formulations.

Thus the total number of decision variables will be the product of number of locations and number of warehouses = 3*2 = 6. Hence the total number of decision variables are 6.