Plants A, B, C, and D produce the same item that is demanded by customers W, X, Y, and Z in the amounts shown in the table. The cost to ship one unit between each combination of plants and customers is also shown in the table

The corporation wishes to minimize the total transportation costs of this assignment problem.
What are the decision variables?
What is the objective function?
What are the constraints?

W X Y Z Total Supply
A $3 $6 $4 $2 22,000
B $7 $10 $8 $6 19,000
C $10 $13 $11 $9 14,000
D $12 $15 $13 $11 15,000
Total Demand 25,000 15,000 18,000 12,000

What will be an ideal response?

Answer: The decision variables are the quantities that are to be shipped between each combination of plant and customer.
SAW, SAX, SAY, SAZ, SBW, SBX, SBY, SBZ, SCW, SCX, SCY, SCZ, SDW, SDX, SDY, SDZ
The objective function will be to minimize cost as a linear sum of all possible combinations of locations. Using S to represent the amount shipped from any plant to any customer:
Min Cost = $3∗SAW + $6∗SAX + $4∗SAY + $2∗SAZ + $7∗SBW + $10∗SBX + $8∗SBY + $6∗SBZ
+ $10∗SCW + $13∗SCX + $11∗SCY + $9∗SCZ + $12∗SDW + $15∗SDX + $13∗SDY + $11∗SDZ

The constraints are that each plant cannot ship more than it produces and that each customer cannot receive less than they want.
Plant A: SAW + SAX + SAY + SAZ ≤ 22,000
Plant B: SBW + SBX + SBY + SBZ ≤ 19,000
Plant C: SCW + SCX + SCY + SCZ ≤ 14,000
Plant D: SDW + SDX + SDY + SDZ ≤ 15,000
Customer W: SAW + SBW + SCW + SDW ≥ 25,000
Customer X: SAX + SBX + SCX + SDX ≥ 15,000
Customer Y: SAY + SBY + SCY + SDY ≥ 18,000
Customer Z: SAZ + SBZ + SCZ + SDZ ≥ 12,000
SAW, SAX, SAY, SAZ, SBW, SBX, SBY, SBZ, SCW, SCX, SCY, SCZ, SDW, SDX, SDY, SDZ ≥ 0