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

question 67

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

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Definitions:

Reception

The act or process of receiving or being received, often referring to the area in hospitals or offices where guests are greeted.

Reaction

A biological, chemical, or physical response to a specific stimulus.

Hearing

The sense through which sounds are perceived, involving the process of detecting and interpreting sound waves.

Visual Sensory Impairment

A reduction or loss of vision that cannot be corrected fully with glasses or contact lenses.