Question 1

The optimal solution to a supply chain management model can be found by solving the standalone separate components of the process.

Accepted Answer

A) True 
 B)False

Question 2

In problem 2, let A = the total amount invested in stocks and B = the total amount invested in bonds.To state that at least 40% of the investment in stocks must be in stock 1, two constraints in the model would be:

Accepted Answer

A) X1 - .4A $\ge$ 0, X2 + X3 + X4 - A = 0 
B) X1 - .4A $\ge$ 0, X1 + X2 + X3 + X4 - A = 0 
C) X1 - .4A - .4B $\ge$0, A + B = 300,000 
D) X1 - .4A - .4B $\le$0, A + B = 300,000 
A) X1 - .4A $\ge$ 0, X2 + X3 + X4 - A = 0 
B) X1 - .4A $\ge$ 0, X1 + X2 + X3 + X4 - A = 0 
C) X1 - .4A - .4B $\ge$0, A + B = 300,000 
D) X1 - .4A - .4B $\le$0, A + B = 300,000

Question 3

Wisconsin State University is planning to advertise its new degree program in Professional Business in several media--television commercials on the local cable station, advertisements in the local community college newspaper, and manning a booth at the county fair.Preliminary estimates are that each television spot will reach 1000 potential students, each newspaper ad will reach 100 potential students, and each day at the county fair will reach 500 potential students.There is a $7500 advertising budget, and the university has negotiated a rate of $825 per ad on the cable station, $85 per ad in the newspaper, and $1150 for a booth at the 3-day county fair.What should be its advertising strategy?

Accepted Answer

( MAX 1000X₁ + 100X₂

Question 4

What is wrong with this model?$\begin{aligned}
\operatorname { MAX } X _ { 1 } + X _ { 2 } - X _ { 3 } & \
\operatorname { ST~X } _ { 1 } & \leq 10 \
X _ { 2 } & \leq 10 \
X _ { 3 } \leq 10 & \
X _ { 1 } - X _ { 2 } & \geq 5 \
X _ { 1 } , X _ { 2 } , X _ { 3 } \geq 0 &
\end{aligned}$

Accepted Answer

The model presented appears to be a line

Question 5

If project 1 is performed then project 2 will not be performed.This can be modeled by the constraint X1 - X2 $\le$ 1, where X1 and X2 are binary variables.

Accepted Answer

A) True 
 B)False

Question 6

The availability of seats for ballgames at Oliver Field is$\begin{array} { l r r r } 
\text { Bleachers } & 4000 \text { seats } & A _ { 1 } & \
\text { General Admission } & 10,000 \text { seats } & A _ { 2 } \
\text { Grandstand } & 10,000 \text { seats } & A _ { 3 } \
\text { Luxury Boxes } & 1000 \text { seats } &A _ { 4 } &
\end{array}$
A1 through A4 represent the attendance in the different seating options at prices X1, X2, X3, and X4. Better seats must cost at least $1 more than the next lower category.  If the team charges $1 per seat, the demand will be 25,000.  For each $1 increase in ticket price, the demand drops by 1000.  The team owner has set up an integer programming model to maximize revenue (not necessarily to sell out).  
What prices should be charged?  Is this a linear programming model?

Accepted Answer

( MAX@#LAT-DLM& X_i(26 - X_i

Question 7

The optimal solution obtained to a maximization integer linear programming model, where the integer requirements are at first ignored, provides a lower bound for the optimal objective function value of the integer model.

Accepted Answer

A) True 
 B)False

Question 8

XLB Sports has 30 franchises (teams).Although most of the teams make an annual profit, some teams report losses.An owner of a team that loses money can still make a profit when he sells the franchise since equity increases have been greater than reported losses.XLB has requested a model to determine which, if any, franchises should be eliminated.The costs associated with team elimination include the buyout of the owner, paying off existing contracts such as ballpark leases, and anticipated legal costs.The objective function is the overall profit of XLB.Because all teams must play on the same day, the number of teams must be an even number.Some teams may lose money at home but help other teams by drawing well in road games. Which of the following is true?

Accepted Answer

A) Teams reporting a loss should be eliminated. 
B) You should use binary variables in a mixed integer model. 
C) The problem can be solved by solving 30 team integer linear programming models. 
D) The problem cannot be modeled. 
A) Teams reporting a loss should be eliminated. 
B) You should use binary variables in a mixed integer model. 
C) The problem can be solved by solving 30 team integer linear programming models. 
D) The problem cannot be modeled.

Question 9

Explain the Excel formula SUMIF(F5:F12,"Daily",B5:B12).

Accepted Answer

(If the value of cell Fx (x =

Question 10

The shadow price for a constraint that expresses that the availability of wood is 3000 board-feet is $0.50, and the range of feasibility is between 2800 and 4000 board-feet.Which of the following is not correct?

Accepted Answer

A) All 3000 board-feet of wood will be used. 
B) If only 2900 board-feet of wood are available, the optimal objective function value will be reduced by $50. 
C) If only 2900 board-feet of wood are available, the optimal solution will not change. 
D) If 6000 board-feet of wood are available, the objective function value will increase by at least $500. 
A) All 3000 board-feet of wood will be used. 
B) If only 2900 board-feet of wood are available, the optimal objective function value will be reduced by $50. 
C) If only 2900 board-feet of wood are available, the optimal solution will not change. 
D) If 6000 board-feet of wood are available, the objective function value will increase by at least $500.

Question 11

Nike will build a factory at Millville or Greenfield, but not both.Alternatively, Nike may choose to build at neither location.The appropriate linear constraint to express this restriction using binary variables Y1 and Y2 is:

Accepted Answer

A) Y1 - Y2 $\le$ 1 
B) Y1 + Y2 $\le$ 1 
C) Y1 + Y2 = 1 
D) Y1 - Y2 $\le$0 
A) Y1 - Y2 $\le$ 1 
B) Y1 + Y2 $\le$ 1 
C) Y1 + Y2 = 1 
D) Y1 - Y2 $\le$0

Question 12

What is Data Envelopment Analysis?

Accepted Answer

A) A linear programming based approach to determine the relative efficiency of entities with similar goals and objectives. 
B) A decision support system that envelops the entire manufacturing and shipping process into an integrated system. 
C) An integer linear programming technique involving solving a series of linear programming models and using the solutions as bounds on the integer solution. 
D) A form of sensitivity analysis that allows the simultaneous changing of multiple decision variable values. 
A) A linear programming based approach to determine the relative efficiency of entities with similar goals and objectives. 
B) A decision support system that envelops the entire manufacturing and shipping process into an integrated system. 
C) An integer linear programming technique involving solving a series of linear programming models and using the solutions as bounds on the integer solution. 
D) A form of sensitivity analysis that allows the simultaneous changing of multiple decision variable values.

Question 13

An assembly line has 4 stations.All laborers are trained to operate all stations.The union contract limits laborers to a 40 hour work week with no overtime.The company is contracted to produce 320 units per week, with a profit of $1000 per unit.Each unit must proceed through all 4 stations in order.However, there is sufficient work in progress inventory to keep all stations busy at all times.Station information is detailed in the following table:$\begin{array}{lcc}
\text { Station } & \text { Time Required Per } & \text { cost to Build the } \
& \text { Unit in minutes } & \text { Station }\
1 & 15 & \$ 5000 \
2 & 20 & \$ 8000 \
3 & 30 & \$ 4000 \
4 & 20 & \$ 10,000
\end{array}$ How many stations of each type does the assembly line require to meet demand?

Accepted Answer

( MIN 5X₁ + 8X₂ +

The optimal solution to a supply chain management model can be found by solving the standalone separate components of the process.

In problem 2, let A = the total amount invested in stocks and B = the total amount invested in bonds.To state that at least 40% of the investment in stocks must be in stock 1, two constraints in the model would be:

What is wrong with this model? MAX +- \leq10 \leq10 \leq10 - \geq5 ,,\geq0

If project 1 is performed then project 2 will not be performed.This can be modeled by the constraint X₁ - X₂ $\le$ 1, where X₁ and X₂ are binary variables.

The optimal solution obtained to a maximization integer linear programming model, where the integer requirements are at first ignored, provides a lower bound for the optimal objective function value of the integer model.

Explain the Excel formula SUMIF(F5:F12,"Daily",B5:B12).

The shadow price for a constraint that expresses that the availability of wood is 3000 board-feet is $0.50, and the range of feasibility is between 2800 and 4000 board-feet.Which of the following is not correct?

Nike will build a factory at Millville or Greenfield, but not both.Alternatively, Nike may choose to build at neither location.The appropriate linear constraint to express this restriction using binary variables Y₁ and Y₂ is:

What is Data Envelopment Analysis?

Introduction to Management Science Models

Introduction to Management Science Models

Network Models

Project Scheduling Models

Decision Models

Forecasting

Inventory Models

Queuing Models

Simulation Models

Quality Management Models

Markov Process Models

Nonlinear Models:dynamic, Goal, and Nonlinear Programming

Filters

Exam 3: Applications of Linear and Integer Programming Models

The optimal solution to a supply chain management model can be found by solving the standalone separate components of the process.

In problem 2, let A = the total amount invested in stocks and B = the total amount invested in bonds.To state that at least 40% of the investment in stocks must be in stock 1, two constraints in the model would be:

What is wrong with this model? MAX +- \leq10 \leq10 \leq10 - \geq5 ,,\geq0

If project 1 is performed then project 2 will not be performed.This can be modeled by the constraint X1 - X2 ≤\le≤ 1, where X1 and X2 are binary variables.

The optimal solution obtained to a maximization integer linear programming model, where the integer requirements are at first ignored, provides a lower bound for the optimal objective function value of the integer model.

Explain the Excel formula SUMIF(F5:F12,"Daily",B5:B12).

The shadow price for a constraint that expresses that the availability of wood is 3000 board-feet is $0.50, and the range of feasibility is between 2800 and 4000 board-feet.Which of the following is not correct?

Nike will build a factory at Millville or Greenfield, but not both.Alternatively, Nike may choose to build at neither location.The appropriate linear constraint to express this restriction using binary variables Y1 and Y2 is:

What is Data Envelopment Analysis?

Introduction to Management Science Models

Introduction to Management Science Models

Network Models

Project Scheduling Models

Decision Models

Forecasting

Inventory Models

Queuing Models

Simulation Models

Quality Management Models

Markov Process Models

Nonlinear Models:dynamic, Goal, and Nonlinear Programming

Filters

If project 1 is performed then project 2 will not be performed.This can be modeled by the constraint X₁ - X₂ $\le$ 1, where X₁ and X₂ are binary variables.

Nike will build a factory at Millville or Greenfield, but not both.Alternatively, Nike may choose to build at neither location.The appropriate linear constraint to express this restriction using binary variables Y₁ and Y₂ is: