Plants in Vienna, Lucerne, Bruhl, and Salzburg produce the same item that is demanded by customers in London, Paris, Milan, and Athens. Customer demand and plant capacity are shown in the bottom row and rightmost column 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. Use the table below to answer the following question(s).
$$\begin{array} { | l | c | c | c | c | c | }
\hline & \text { London } & \text { Paris } & \text { Milan } & \text { Athens } & \text { Total Capacity } \
\hline \text { Vienna } & \$ 19 & 16 & 3 & 8 & 600 \
\hline \text { Lucerne } & 15 & 17 & 17 & 13 & 500 \
\hline \text { Bruhl } & 13 & 18 & 18 & 7 & 400 \
\hline \text { Salzburg } & 16 & 18 & 18 & 7 & 470 \
\hline \text { Total Demand } & 500 & 450 & 620 & 400 & \
\hline
\end{array}$$
-What of these equations would be part of the appropriate objective function?

Question

Plants in Vienna, Lucerne, Bruhl, and Salzburg produce the same item that is demanded by customers in London, Paris, Milan, and Athens. Customer demand and plant capacity are shown in the bottom row and rightmost column 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. Use the table below to answer the following question(s).
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & \text { London } & \text { Paris } & \text { Milan } & \text { Athens } & \text { Total Capacity } \
\hline \text { Vienna } & \$ 19 & 16 & 3 & 8 & 600 \
\hline \text { Lucerne } & 15 & 17 & 17 & 13 & 500 \
\hline \text { Bruhl } & 13 & 18 & 18 & 7 & 400 \
\hline \text { Salzburg } & 16 & 18 & 18 & 7 & 470 \
\hline \text { Total Demand } & 500 & 450 & 620 & 400 & \
\hline
\end{array}$$
-What of these equations would be part of the appropriate objective function?

Quizplus · Accepted Answer

The appropriate objective function should include the transportation costs for all shipments. Therefore, the equation that includes the cost for each shipment (i.e. $19∗ S_VL + $16∗ S_VP + $3∗ S_VM + $8∗ S_VA) is the most suitable option.

Plants in Vienna, Lucerne, Bruhl, and Salzburg Produce the Same