Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | }
\hline \text { Transpartation } & & & & & \
\text { Model } & & & & & \
\hline & & & & & \
\hline \text { Data } & & & & & \
\hline & \text { Distribution } & & & & \
& \text { Center } & & & & \
\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \
\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \
\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \
\hline \text { Dernand } & 175 & 325 & 480 & 950 & \
\hline
\end{array}$$ Answer the following questions) using a linear optimization model.
-Which of the following is the constraint of nonnegativity for all values of i and j?
A) 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 / 10.75 X21 +15.16 X22 + 9.65 X23 +18.5 X24 $\le$ 0
B) Xij$\ge$ 0, for all i and j
C) Xij $\le$ 0, for all i and j
D) $\left( 13 X _ { 11 } + 15.25 X _ { 12 } + 10.99 X _ { 13 } + 18.48 X _ { 14 } - 10.75 X _ { 21 } + 15.16 X _ { 22 } + 9.65 X _ { 23 } + 18.5 X _ { 24 } \right) ( 1,250 / 750 ) \leq 0$

Question

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Transpartation } & & & & & \
\text { Model } & & & & & \
\hline & & & & & \
\hline \text { Data } & & & & & \
\hline & \text { Distribution } & & & & \
& \text { Center } & & & & \
\hline \text { Plant }  & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \
\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \
\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \
\hline \text { Dernand } & 175 & 325 & 480 & 950 & \
\hline
\end{array}$$ Answer the following questions) using a linear optimization model.
-Which of the following is the constraint of nonnegativity for all values of i and j?
A) 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 / 10.75 X21 +15.16 X22 + 9.65 X23 +18.5 X24 $\le$ 0
B) Xij$\ge$ 0, for all i and j
C) Xij $\le$ 0, for all i and j
D) $\left( 13 X _ { 11 } + 15.25 X _ { 12 } + 10.99 X _ { 13 } + 18.48 X _ { 14 } - 10.75 X _ { 21 } + 15.16 X _ { 22 } + 9.65 X _ { 23 } + 18.5 X _ { 24 } \right) ( 1,250 / 750 ) \leq 0$

Quizplus · Accepted Answer

The nonnegativity constraint in linear optimization models ensures that the decision variables, in this case, the amounts shipped from each plant to each distribution center (Xij), cannot be negative. This is because you cannot ship a negative quantity of goods.

Use the Table Below to Answer the Following Questions) Answer the Following Questions) Using a Linear Optimization Model