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Plants A, B, C, and D Produce the Same Item

Question 82

Essay

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?
WXYZ Total Supply  A $3$6$4$222,000 B $7$10$8$619,000 C $10$13$11$914,000 D $12$15$13$1115,000 Total Demand 25,00015,00018,00012,000\begin{array} { | c | c | c | c | c | c | } \hline & \mathbf { W } & \mathbf { X } & \mathbf { Y } & \mathbf { Z } & \text { Total Supply } \\\hline \text { A } & \$ 3 & \$ 6 & \$ 4 & \$ 2 & 22,000 \\\hline \text { B } & \$ 7 & \$ 10 & \$ 8 & \$ 6 & 19,000 \\\hline \text { C } & \$ 10 & \$ 13 & \$ 11 & \$ 9 & 14,000 \\\hline \text { D } & \$ 12 & \$ 15 & \$ 13 & \$ 11 & 15,000 \\\hline \text { Total Demand } & 25,000 & 15,000 & 18,000 & 12,000 & \\\hline\end{array}

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The decision variables are the quantitie...

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