Define the decision variables for this situation

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision.

The table below shows the cost ($ per item) for shipping from each DC to each region.

Region
DC A B C D
1 1 3 3 2
2 2 4 1 3
3 3 2 2 3

The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units.

Answer: y1 = 1 if DC1 is selected, 0 otherwise
y2 = 1 if DC2 is selected, 0 otherwise
y3 = 1 if DC3 is selected, 0 otherwise
x1A = quantity shipped from DC 1 to Region A
x1B = quantity shipped from DC 1 to Region B
x1C = quantity shipped from DC 1 to Region C
x1D = quantity shipped from DC 1 to Region D
x2A = quantity shipped from DC 2 to Region A
x2B = quantity shipped from DC 2 to Region B
x2C = quantity shipped from DC 2 to Region C
x2D = quantity shipped from DC 2 to Region D
x3A = quantity shipped from DC 3 to Region A
x3B = quantity shipped from DC 3 to Region B
x3C = quantity shipped from DC 3 to Region C
x3D = quantity shipped from DC 3 to Region D