Use the table below to answer the following question(s).
The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand.
Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas,
i = 2 represents Atlanta, j = 1 represents Houston, and so on. $\begin{array}{|l|l|l|l|l|l|}\hline \text { Transportation } & \
\text { Model } & \
\hline & \
\hline \text { Data } & \
\hline & \begin{array}{l}
\text { Distribution } \
\text { Center }
\end{array} \
\hline \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jacksonville } & \text { Memphis } & \text { Capacity } \
\hline \text { Dallas } & 13.00 & 15.25 & 10.99 & 18.48 & 1250 \
\hline \text { Atlanta } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \
\hline \text { Demand } & 175 & 325 & 480 & 950 & \
\hline
\end{array}$ Answer the following question(s) using a linear optimization model.
-Which of the following is the objective function for cost minimization?
A) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 / 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24
B) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 + 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24
C) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 - 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24
D) minimize cost = (13 X11 +15.25 X12 +10.99 X13 +18.48 X14 - 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24 )(1,250 / 750)

Question

Quizplus · Accepted Answer

The objective function for cost minimization is to minimize the total transportation cost. The total transportation cost is the sum of the unit transportation cost multiplied by the amount shipped between each plant and distribution center. The objective function is therefore:minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 + 10.75 X21 +15.16 X22 +9.65 X23 +18.5 X24

Use the Table Below to Answer the Following Question(s) Answer the Following Question(s) Using a Linear Optimization Model