Question 1

constraints essentially state that input = output and ensure that the flow of material or money is accounted for at locations or between time periods.
A) Requirements
B) Proportional relationships
C) Balance
D) Limitations

Accepted Answer

Constraints ensure balance between input and output, ensuring that the flow of material or money is accounted for. Requirements refer to what is needed or desired, proportional relationships relate two or more quantities with a constant ratio or proportionality, and limitations refer to restrictions or boundaries on a system.

Question 2

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 gives the constraint for the demand met at a distribution center?
A) X11 + X21 = 1,250
B) X13 + X23 ? 210
C) X13 + X23 = 770
D) X13 + X23 = 480

Accepted Answer

The constraint for the demand met at the Jacksonville distribution center is that the total amount shipped from both Dallas and Atlanta to Jacksonville (X13 + X23) must equal the demand at Jacksonville, which is 480.

Question 3

Which of the following is an example of a simple bounds constraint?
A) confirming that production does not go beyond a certain unit value
B) reducing production due to scarcity of resources
C) meeting targets for a specific sales job
D) equaling production in September with the resources available at the end of August

Accepted Answer

A simple bounds constraint sets a limit on a certain variable or production output. In this case, the constraint is limiting production to not go beyond a certain unit value.

Question 4

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.
-From the Sensitivity Report on the model, to which of the following cities can Atlanta not ship to without reducing unit cost of production?
A) Houston
B) San Jose
C) Jacksonville
D) Memphis

Accepted Answer

The answer of Use the table below to answer the...

Question 5

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.
-Based on the Sensitivity Report on the model, which of the following is the savings on a reduction of demand of 2 units at Jacksonville?
A) $2.5
B) $1.25
C) $19.48
D) $16.98

Accepted Answer

The answer of Use the table below to answer the...

Question 6

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 constraint for total amount shipped from Dallas?
A) X11 + X12 + X13 + X14 ? 1,250
B) X21 + X22 + X23 + X24 ? 1,250
C) X21 + X22 + X23 + X24 ? 750
D) X11 + X12 + X13 + X14 - X21 + X22 + X23 + X24 ? 850

Accepted Answer

The constraint for total amount shipped from Dallas is X11 + X12 + X13 + X14 ? 1,250 because this constraint ensures that the total amount shipped from Dallas does not exceed the plant's capacity of 1,250 units.

Question 7

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.
-According to the transportation model, what is the total shipment from Dallas?
A) 750
B) 1,180
C) 430
D) 950

Accepted Answer

The total shipment from Dallas is equal to the sum of shipments from Dallas to each distribution center. From the given table, we can see that the shipments from Dallas to Houston, San Jose, Jacksonville, and Memphis are 175, 325, 480, and 200, respectively. Therefore, the total shipment from Dallas is 175 + 325 + 480 + 200 = 1,180.

Question 8

Which of the following would be considered as an example of a proportional relationships constraint?
A) making certain that only a certain amount of units are produced
B) guaranteeing that a certain amount of workforce will be available for a certain month
C) balancing the input to the output during production
D) ensuring that the budget allocated to marketing is thrice that of research and development

Accepted Answer

A proportional relationship constraint involves maintaining a specific ratio between two quantities, such as ensuring the marketing budget is three times that of research and development.

Question 9

Problem statements such as the amount of material used in production cannot exceed the amount available in inventory would be categorized as a constraint.
A) proportional relationships
B) limitations
C) requirements
D) simple bounds

Accepted Answer

The statement is describing a limitation, which is a type of constraint that defines a boundary or restriction on a certain aspect of a problem. Proportional relationships refer to the mathematical relationship between two variables, requirements are specific needs or expectations that must be met, and simple bounds refer to straightforward limits or boundaries.

Question 10

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.
-According to the Sensitivity Report, which of the following is true if the capacity at Atlanta is increased by 230 units?
A) the total cost can be reduced by $.09 per unit
B) the total cost at Atlanta increases by $9
C) the total cost per unit will reduce by $.09 to Memphis
D) the shadow price at Atlanta will increase to $0.09

Accepted Answer

Increasing the capacity at Atlanta by 230 units will reduce the total cost by $0.09 per unit, as indicated by the shadow price for the capacity constraint at Atlanta.

Question 11

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.
-According to the transportation model, which of the following is the amount shipped from Dallas to San Jose?
A) 0
B) 95
C) 230
D) 325

Accepted Answer

The answer of Use the table below to answer the...

Question 12

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.
-According to the transportation model, which of the following is the amount shipped from Dallas to Houston?
A) 0
B) 175
C) 1,180
D) 750

Accepted Answer

The answer of Use the table below to answer the...

Question 13

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)

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

Question 14

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.
-According to the Sensitivity report on the model, by what price should the unit cost of shipment reduce to make shipment from Dallas to Houston feasible?
A) $8.68
B) $2.16
C) $10.84
D) $3.41

Accepted Answer

The sensitivity report indicates the shadow price or reduced cost for non-basic variables. The reduced cost for Dallas to Houston must be reduced by $2.16 to become feasible.

Question 15

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 constraint for total amount shipped from Atlanta?
A) X11 + X12 + X13 + X14 - X21 + X22 + X23 + X24 ? 850
B) X21 + X22 + X23 + X24 ? 750
C) X21 + X22 + X23 + X24 ? 1250
D) X11 + X12 + X13 + X14 ? 1250

Accepted Answer

The constraint for total amount shipped from Atlanta is X21 + X22 + X23 + X24 ? 750, which represents the capacity of the Atlanta plant.

Question 16

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.
-According to the transportation model, what is the total cost incurred by Riviera Transport Company?
A) $29,016.95
B) $26,698.95
C) $20,331.35
D) $41,978.75

Accepted Answer

The total cost is the sum of the products of the unit transportation costs and the amounts shipped. From the given table, we have:Total cost = (13 * X11) + (15.25 * X12) + (10.99 * X13) + (18.48 * X14) + (10.75 * X21) + (15.16 * X22) + (9.65 * X23) + (18.50 * X24)The optimal solution to the transportation model is:X11 = 175X12 = 0X13 = 480X14 = 600X21 = 0X22 = 325X23 = 0X24 = 425Substituting these values into the total cost equation, we get:Total cost = (13 * 175) + (15.25 * 0) + (10.99 * 480) + (18.48 * 600) + (10.75 * 0) + (15.16 * 325) + (9.65 * 0) + (18.50 * 425)= $29,016.95Therefore, the total cost incurred by Riviera Transport Company is $29,016.95.

Question 17

Problem statements such as production must be sufficient to meet promised customer orders would be categorized as a constraint.
A) limitations
B) requirements
C) proportional relationships
D) balance

Accepted Answer

Constraints in problem statements are often categorized as requirements because they specify conditions that must be met, such as fulfilling customer orders.

Question 18

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.
-According to the transportation model, what is the amount shipped from Atlanta to Memphis?
A) 480
B) 0
C) 230
D) 950

Accepted Answer

The transportation model minimizes the total transportation cost by finding the optimal shipping quantities between plants and distribution centers. According to the model, the optimal solution is to ship 0 units from Atlanta to Memphis.

Question 19

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.
-According to the transportation model, what is the amount shipped from Atlanta to Jacksonville?
A) 950
B) 480
C) 0
D) 95

Accepted Answer

The demand for Jacksonville is 480, and Atlanta has the lowest shipping cost to Jacksonville. Therefore, it is optimal to ship the entire demand of 480 from Atlanta to Jacksonville.

Question 20

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 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 ? 0
B) Xij ? 0, for all i and j
C) Xij ? 0, for all i and j
D) $\left( 13 X _ { 11 } + 15.25 X _ { 12 } + 10.99 X _ { 13 } + 18.48 X _ { 14 } - 10.75 X _ { 21 } + 15.16 X _ { 22 } + 9.65 X _ { 23 } + 18.5 X _ { 24 } \right) ( 1,250 / 750 ) \leq 0$

Accepted Answer

The constraint of nonnegativity for all values of i and j is Xij ? 0, for all i and j. This constraint ensures that the amount shipped from plant i to distribution center j is nonnegative.

Quiz 14: Applications of Linear Optimization

constraints essentially state that input = output and ensure that the flow of material or money is accounted for at locations or between time periods.

Which of the following is an example of a simple bounds constraint?

Which of the following would be considered as an example of a proportional relationships constraint?

Problem statements such as the amount of material used in production cannot exceed the amount available in inventory would be categorized as a constraint.

Problem statements such as production must be sufficient to meet promised customer orders would be categorized as a constraint.