BUSI508_Week2_Assignment SCORE 100 PERCENT

On the tab labeled "Original Problem", I have provided the modeling of Problem #17 on Page 307.  Carefully read the statement of the problem in the textbook and then review the model and solver set up to familiarize yourself with the integration of the LP into Excel.  Cells that are highlighted in RED should not be changed by students throughout the exercise (though some will change automatically as the problem is re-solved); however, you are free to change any of the GREEN cells as necessary to answer the questions related to the problem.  There are three questions; each question has a corresponding tab in this file.  Each question should be viewed independently from the others (i.e., each of the three questions should be treated as a stand alone change from the original problem.  So, please make the required changes and solve the updated model for each question).  To answer each question, you will be required to change information in the respective spreadsheet and then load the solver from scratch similar to what you observed in the ASPE videos.  In your response to each question, you should begin with a written sentence(s) that explains how you manipulated the original problem followed by the resulting optimal solution after re-solving the model.   Questions 1 and 2 are worth 3 points; Question 3 is worth 4 points.  Questions should be answered on the respective tabs and typed in unbolded black font right after the statement of the question.  Good luck, and as always...HAVE FUN!


Question 1  (3 points).  Managment has incorporated a new fee structure for its production process.  They have decided to reduce all fixed costs by 10% (round all decimals up to the next whole dollar) and increase all variable costs by $4.  What is the new optimal solution? HINT:  This scenario requires you to make changes in the B and C columns then load the solver.  When you change the
values in Column B, you should round them to the nearest whole dollar.  The solver setup will be the same as shown on the Original Problem.

Question 2  (3 points).  Machine 4 suffered a catastrophic failure injuring an employee.  The machine cannot be used for the next six weeks until parts are received and the machine is fixed.  In light of this issue and given that Machines 3 and 6 do not contribute to the optimal solution in the original problem, management wants to ensure both machines (3 and 6) are used while Machine 4 is under repair.  Management wants Machines 3 and 6 to produce at least 110 shoes per machine.  What is the resulting optimal solution (give total cost only after re-solving the problem). HINT:  This scenario does not require any change in the spreadsheet.  The solver setup will be the same as shown on the Original Problem tab but will also require additional constraints to incorpoate this new production scenario.  Once you have made this change and loaded the solver, solve the problem and report your updated solution.

Question 3  (4 points).   With new car sales down due to the poor economy and as a supplier of brake shoes for older vehicles, Radford has received an order for 2,600 new brake shoes (this is the new "required" value).  To ensure their best opportunity for success in meeting this new requirement, they plan to produce 25% to 45% of the required total on machines not normally used (Machines 3 and 6).  The remainder of the load (i.e., the difference between 2,600 and the total number of brake shoes made on Machines 3 and 6 combined) must be split over the machines such that each machine makes at least 10% of the difference.  What is the optimal solution and cost of this strategy (give both only after re-solving the model). HINT:  I would start this problem by changing Cell E15 to 2600.  Next, I would create a new cell in the spreadsheet that computes 25% of the required total and another cell that computes 45% of the required total.  A third new cell should compute the sum of shoes made by Machines 3 and 6 combined.  Finally, in the spreadsheet, I would create another new cell that computes 10% of the difference between the required number of shoes and total made by Machines 3 and 6.  From here, the solver setup will be the same as shown on the Original Problem tab but will also require additional constraint(s) to incorpoate this new production scenario.  The new constraints will be comparisons of the decision variables with the new cells created per my hint.  Once you have made this change and loaded the solver, solve the problem and report your updated optimal solution and total cost.

 

  

BUSI508_Week1_Assignment SCORE 100 PERCENT

Welcome to your first Excel Exercise!  Your first assignment is to ensure you have activated the Solver that is within your Excel software.  This assignment should be completed after you read Chapters 1 and 2 and watched the video I have identified on the Assignment tab.  Please click over to the Assignment tab (bottom left hand corner of this page) and please respond to the five questions.  Have a great week and please let me know if there is anything I can do for you!

Please respond to these five questions and submit this file to me via the course dropbox no later than midnight Central Time Sunday night.  Please type your answers in unbolded black font directly below the question.

1.  (2 Points)  Watch the following video:  https://www.youtube.com/watch?v=KcM2-VEwhcY&t=67s.  After watching the video, have you successfully enabled Solver?

2.  (2 Points)  In the video, in which cell is the Objective Function?

3.  (2 Points)  In the video, in which cells are the Decision Variables?

4.  (2 Points)  In the video, what is the value calcuated in cell E16?

5.  (2 Points) From the assigned readings and video, once a linear programming model is solved and the value of the objective function is obtained, is that value considered the optimal solution?  Or, are the values of the associated decision variables considered the optim

o  

al solution?

BUSI508 Week 8 ReturnsSimulation SCORE 100 PERCENT

Regardless of how old you are, you are probably thinking about retirement and making sure you have enough money to sustain your lifestyle.  Let's assume that all of us are doing so by investing in the stock market.  What are the mathematical techniques we could use to estimate our retirement nest egg?  One way to do this is to use a consistent, average market return over the last 90 years or so and a consistent annual investment.  What are the limitations of that approach?  Below is a graphic that shows annual stock market returns since 1921.  Clearly, the market has not experienced consistent returns over the past 97 years!!  The take-away is:

Retirement Nest Egg ($) = f(annual investment, stock market return)

You have control over the amount you invest but don't control market performance.  How does a simulation assist us in addressing retirement planning?

Video:  https://www.youtube.com/watch?v=7Ux-FB4OpTs

  

BUSI508 Week 8 Discussion SCORE 100 PERCENT

In the Content area of Week 8, there is a file titled "Returns Simulation." Open the file and watch the associated video so that you have an understanding of how Excel was used to generate the simulation. After watching the video, select the Simulation tab and hit the F9 key on your computer 10 times. On the 10th trial, record the monetary value you see in Cell M4 and post it on the discussion board. Additionally, give an example of a scenario where simulation would be an effective approach to understand the behavior of a dependent variable. Do not repeat investment planning as an example of such a scenario!

 

BUSI508 Week 7 Excel Exercise 6 SCORE 100 PERCENT

Question 1 (4 Points) On the tab labeled "CPM Network", you will find a skeleton AON network of Problem 10.  Enter the activities (A through I) in the cells highlighted in green according to the statement of the problem; there is only one solution based on the statement of the problem.  Do not change any of the formatting in the CPM Network tab, just enter the letters A through I, one per cell, according to the statement of the problem.  In the network model I have provided on the CPM Network tab, what do the green cells represent and what do the yellow lines represent?

 
Question 2 (4 Points) On the tab labeled "CPM Calculation" you will find a matrix where I have started the computation to find the critical path for the project by calculating the early start/finish and late start/finish times.  Discuss the calculations necessary to finish the early start (EST) and early finish (EFT) columns as part of the Forward Pass process.  For any blank cells in the forward pass, enter the correct value on the "CPM Calculation" sheet.  What is the earliest time the project can be completed (# of days)?  Please note the spreadsheet is not set up with formulas for calculations; you must manually complete these calculations and enter the appropriate values in the spreadsheet.    

Question 3 (4 Points) On the tab labeled "CPM Calculation" you will find a matrix where I have started the computation to find the critical path for the project by calculating the early start/finish and late start/finish.  Discuss the calculations necessary to finish the late finish (LFT) and late start (LST) columns as part of the Backward Pass process.  For any blank cells in the backward pass, enter the correct value on the "CPM Calculation" sheet.  Please note the spreadsheet is not set up with formulas for calculations; you must manually complete these calculations and enter the appropriate values in the spreadsheet.

Question 4 (4 Points) After completing Questions 2 and 3, go back to the "CPM Calculation" tab and compute the slack for each task then state (here) the activities on the critical path.

Question 5 (4 Points) After completing the Microsoft Project portion of this exercise, does the overall duration of the project and critical path agree with what you have calculated here?

 

BUSI508 Week 7 Discussion SCORE 100 PERCENT

Program Success/Failure and Personality

Fundamentally, program management boils down to three things:  completing a project within cost, on time, and delivering "whatever" to meet the desired purpose established for the project.  If  you've been a program manager in the past, discuss a project you worked on, whether it was a success or failure and why you categorize it as such.  If you have never been a program manager, you will as an MBA!  I contend that being a program manager is a personality - what kind of personality are you going to be to ensure the success of your team and your project?

 

BUSI508 Week 7 Case Review 5 SCORE 100 PERCENT

Question 1 (16 Points) On the tab labeled "CPM Network", you will find a skeleton AON network model for Case 15.3.  The layout includes the activities required to complete the project discussed in the case.  Based on the reading of the problem, enter the arcs (lines) to connect the activities according to the problem.  In the model you will note I left a single arc (line) for you.  You may copy/paste this as many times as required to assemble your model.  You can adjust the slope and length of the line as required by clicking your mouse on the line itself.  Do not change any other formatting in the CPM Network tab, just enter the arcs according to the statement of the problem.  In the network model I have provided on the CPM Network tab, what do the lines you entered represent?

Question 2 (16 Points) On the tab labeled "CPM Calculation" you will find a matrix where I have listed the activities for the project.  By reading the problem carefully, enter the predecessors and the associated durations (Days Required) for each task.  Do not change the predecessors I have entered for the "Finish" activity.  What is the definition of a predecessor?

Question 3 (16 Points) On the tab labeled "CPM Calculation" complete the calculations necessary to show the early start (EST) and early finish (EFT) times for each activity.  Please note the spreadsheet is not set up with formulas for calculations; you must manually complete these calculations and enter the appropriate values in the spreadsheet.  What is the duration of the project?  

Question 4 (16 Points) On the tab labeled "CPM Calculation" complete the calculations necessary to show the late finish (LFT) and late start (LST) times for each activity.  Please note the spreadsheet is not set up with formulas for calculations; you must manually complete these calculations and enter the appropriate values in the spreadsheet.  Does the duration of the project differ from the duration found in the forward pass?

Question 5 (16 Points) After completing Questions 3 and 4, go back to the "CPM Calculation" tab and in the Critical Path column (column J), compute the slack for each activity.  What activities are on the critical path?  Using the information you have assembled in the "CPM Calculation" tab, enter this information in Microsoft Project.  On Line 1 of your Project file, title this summary task as Case 15.3 Duration and ensure all subsequent tasks are entered as subtasks (indented).  Do the critical path and duration match what you calculated here in the Excel file?

 

BUSI508 Week 6 Excel Exercise 5

Question 1 (4 Points) Assuming an arrival and service rate of one truck per hour, is it a feasible for Seabreeze to employ just one server?  Why or why not?

Question 2 (4 Points) Assuming an arrival rate of one truck per hour, a service rate of two trucks per hour, and a total of two employees, what is the total hourly cost of when conisdering employee salaries/benefits and the hour cost to the company for having a truck sitting at the dock for loading or unloading?  Recall, the cost of each employee is $21/hour and when considering the cost to the company for having a truck in the queue, the hourly cost is $35/hour though prorated for the total time spent in the system

Question 3 (4 Points) Assuming an arrival rate of one truck per hour, a service rate of three trucks per hour, and a total of three employees, what is the total hourly cost of when conisdering employee salaries/benefits and the hour cost to the company for having a truck sitting at the dock for loading or unloading?  Recall, the cost of each employee is $21/hour and when considering the cost to the company for having a truck in the queue, the hourly cost is $35/hour though prorated for the total time spent in the system.  

Question 4 (4 Points) Assuming an arrival rate of one truck per hour, a service rate of four trucks per hour, and a total of four employees, what is the total hourly cost of when conisdering employee salaries/benefits and the hour cost to the company for having a truck sitting at the dock for loading or unloading?  Recall, the cost of each employee is $21/hour and when considering the cost to the company for having a truck in the queue, the hourly cost is $35/hour though prorated for the total time spent in the system


Question 5 (4 Points) What is the best employment strategy for Seabreeze, 1, 2, 3, or 4 hourly employees?  Why?  

 

BUSI508 Week 6 Case Review 4 -Chapter 13, Page 751, Case 13.1I

Question 1 (16 Points) On the tab labeled "Arrival" you will see the number of calls received for the 500 randomly chosen hours at each of the five precincts.  Compute the Arrival Rate for each precinct and enter those values (to 2 decimal places) accordingly in the matrix to the left.  On the tab labeled "Service", you will see the service times (in minutes) for each call logged at each of the five precincts during the sampled period.  Note that each precinct logged a different number of calls.  For each precinct, compute the Service Rate and enter those values (to 2 decimal places) accordingly in the matrix to the left.  As a reminder, both rates should be entered based on the number per hour; be particularly careful in computing the service rates!!


Question 2 (16 Points) For each precinct, you will note I have entered the number of servers currently serving.  After completing Question 1, enter the Arrival and Service Rates and # of Servers for each precinct into Q.xls and obtain the queue characteristics.  Copy and paste the results from each Q.xls run into the appropriate column in the matrix to the left.  Report all values to 2 decimal places.

Question 3 (16 Points) Based on expected wait times in the queue before speaking with an operator, which precinct is currently most efficient?  In answering this questions be sure to include the wait time in minutes.
Precinct "B" is the most efficient. Expected time in queue for "B" is 2.40 minutes, which is minimum among all precincts.

Question 5 (16 Points) It is the city's goal to limit the before speaking to a 911 operator to two minutes or less.  In the Number of Added Servers line to the left, state the minimum number of servers that must be added to each precinct to meet the city's goal of two minutes or less in the queue before speaking with an operator.  Discuss how you arrived at each answer.

  

BUSI508 Week 5 Chapter 9, Page 496, Case 9.2

Question 1 (16 Points):  On the Data tab, you will find the results listed by the counties each candidate won during the election (Bush in red and Gore in blue).  Considering only the counties won by Bush, on a new tab labeled "Bush Scatter", build a scatterplot with Gore totals as the independent variable and Bush totals as the dependent variable.  What is the associated regression equation and goodness of fit measure?

Question 2 (16 Points):  On the Data tab, you will find the results listed by the counties each candidate won during the election (Bush in red and Gore in blue).  Considering only the counties won by Gore, on a new tab labeled "Gore Scatter", build a scatterplot with Bush totals as the independent variable and Gore totals as the dependent variable.  What is the associated regression equation and goodness of fit measure?

Question 3 (16 Points):  Bush won Brevard County with 114,858 votes.  Using the results in Question 1 above, estimate the total number of votes President Bush should have received given the actual number of votes won by Gore in the same county.  What is the residual as compared to the actual number of votes won by Bush?

Question 4 (16 Points):  Now we want to estimate the number of votes Buchanan should have received given the votes received by both Bush and Gore in the counties won by each candidate.  On a new tab labeled "Bush Multiple" use both the Bush and Gore totals from the counties won by  Bush as independent variables along with the asociated Buchanan totals as the dependent variable and develop the regression equation.  On a new tab labeled "Gore Multiple" use both the Bush and Gore totals from the counties won by Gore as independent variables along with the asociated Buchanan totals as the dependent variable and develop a second regression equation.  After completing these analyses, which data, either the counties won by Bush or the counties won by Gore, best estimate the number of votes expected for Buchanan.  Clearly state the reasoning behind your choice of data selection.  

Question 5 (16 Points):  Based on the best model you found in Question 4, refer back to the Data tab and note that each candidate has a row where the entries are in white font.  If the best model you found in Question 4 was based off the counties won by Bush, estimate the number of votes Buchanan should have received in Okeechobee County based on the votes received by Bush and Gore.  If the best model you found in Question 4 was based off the counties won by Gore, estimate the number of votes Buchanan should have expected in Palm Beach County based on the votes received by Bush and Gore.  What isthe residual value in the predicted number of votes as compared to the actual number of votes received by Buchanan?

  

BUSI508 Week 4 Discussion SCORE 100 PERCENT

Do an Internet search on "network modeling." Find an article where a business of any industry used network modeling to solve a tough problem. In response, you are required to post the Internet link and provide a 400-500 word statement summarizing the company's issue and resolution. Conduct additional research and assess the company's challenges and successes in using network modeling and the effectiveness of the particular model chosen. Before you choose your initial article, please make sure one of your classmates has not posted a similar application. For example, there are several articles on the Internet about utility companies using network modeling to optimize distribution.

 

BUSI508 Week 4 Assignment SCORE 100 PERCENT

On the tab labeled "Network Diagram", I have provided a visual representation of the network for Problem #9 on Page 227.   On the tab labeled "Production Plan," you will see the integration of the general framework of the network integrated into Excel.    Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  
+

On the tab labeled "Network Diagram", I have provided a visual representation of the network
On the tab labeled "Network Diagram", I have provided a visual representation of the network for Problem #9 on Page 227.   On the tab labeled "Production Plan," you will see the integration of the general framework of the network integrated into Excel.    Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

Proceed to the Solutions tab where you will find five questions.  To answer each question, you will be required to consult the Network Diagram, enter values into the spreadsheet and then transfer some information to ASPE.  In your response to each question, start by entering the appropriate information into the spreadsheet or ASPE and then answer the remainder of the question in a written response.  Each question is worth 4 points:  2 points for making the correct inputs to the spreadsheet or ASPE and 2 points for a clear, concise, grammatically
Good luck, enjoy the collaboration with your teammate and as always...HAVE FUN! '

1[- t.ky\9ohls,dflghbn. ;/tion 1 (4 Points):  In the Column labeled "To" (Column D), fill in the numbers of the appropriate nodes based on your review of the network diagram.  The Cost information in the model should be helpful in filling out this column.  Describe what the "To" nodes represent in the model.  

Question 2 (4 Points): In the Column labeled "Supply/Demand" (Column I), fill in the  appropriate Supply (should be typed as a negative number) or Demand (should be typed in as a positive number) for the respective node.  For example, Cell I6 would be the supply or demand at Node 1.  Describe in detail the interpretation of the value in Cell I10.


Question 3 (4Points):  There are two constraints in this problem:  first is the relationship between the Net Flow and Supply/Demand.  Describe this relationship and then incorporate the constraint in RSPE.
Constraint:


Question 4 (4 Points):  The second constraint is the relationship between the Flow (decision variables) and the minimum number of units that must be moved from each node.  Describe this relationship and then incorporate the constraint in RSPE.
Flow ($B6:$B16) >= Min ($A$6:$A$14)

Question 5 (4 Points):  The formula for the Objective Function in Cell E16 is missing.  Enter the appropriate formula and describe what is being calculated in that cell.  Once you have entered the formula and the two constraints from Questions 3 and 4 above, solve the model.  What is the optimal solution?
,36321;'452/582
152., 6ilujyk,./or Problem #9 on Page 227.   On the tab labeled "Production Plan," you will see t'p,mhgfdcqwsdrftvgbnm./he integration of the general framework of the network integrated into Excel.    Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

Proceed to the Solutions tab where you will find five questions.  To answer each question, you will be required to consult the Network Diagram, enter values into the spreadsheet and then transfer some information to ASPE.  In your response to each question, start by entering the appropriate information into the spreadsheet or ASPE and then answer the remainder of the question in a written response.  Each question is worth 4 points:  2 points for making the correct inputs to the spreadsheet or ASPE and 2 points for a clear, concise, grammatically
Good luck, enjoy the collaboration with your teammate and as always...HAVE FUN! '

1[- t.ky\9ohls,dflghbn. ;/tion 1 (4 Points):  In the Column labeled "To" (Column D), fill in the numbers of the appropriate nodes based on your review of the network diagram.  The Cost information in the model should be helpful in filling out this column.  Describe what the "To" nodes represent in the model.  

Question 2 (4 Points): In the Column labeled "Supply/Demand" (Column I), fill in the  appropriate Supply (should be typed as a negative number) or Demand (should be typed in as a positive number) for the respective node.  For example, Cell I6 would be the supply or demand at Node 1.  Describe in detail the interpretation of the value in Cell I10.


Question 3 (4Points):  There are two constraints in this problem:  first is the relationship between the Net Flow and Supply/Demand.  Describe this relationship and then incorporate the constraint in RSPE.
Constraint:


Question 4 (4 Points):  The second constraint is the relationship between the Flow (decision variables) and the minimum number of units that must be moved from each node.  Describe this relationship and then incorporate the constraint in RSPE.
Flow ($B6:$B16) >= Min ($A$6:$A$14)

Question 5 (4 Points):  The formula for the Objective Function in Cell E16 is missing.  Enter the appropriate formula and describe what is being calculated in that cell.  Once you have entered the formula and the two constraints from Questions 3 and 4 above, solve the model.  What is the optimal solution?
,36321;'452/582
152., 6ilujyk,./On the tab labeled "Network Diagram", I have provided a visual representation of the network for Problem #9 on Page 227.   On the tab labeled "Production Plan," you will see the integration of the general framework of the network integrated into Excel.    Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

Proceed to the Solutions tab where you will find five questions.  To answer each question, you will be required to consult the Network Diagram, enter values into the spreadsheet and then transfer some information to ASPE.  In your response to each question, start by entering the appropriate information into the spreadsheet or ASPE and then answer the remainder of the question in a written response.  Each question is worth 4 points:  2 points for making the correct inputs to the spreadsheet or ASPE and 2 points for a clear, concise, grammatically
Good luck, enjoy the collaboration with your teammate and as always...HAVE FUN! '

1[- t.ky\9ohls,dflghbn. ;/tion 1 (4 Points):  In the Column labeled "To" (Column D), fill in the numbers of the appropriate nodes based on your review of the network diagram.  The Cost information in the model should be helpful in filling out this column.  Describe what the "To" nodes represent in the model.  

Question 2 (4 Points): In the Column labeled "Supply/Demand" (Column I), fill in the  appropriate Supply (should be typed as a negative number) or Demand (should be typed in as a positive number) for the respective node.  For example, Cell I6 would be the supply or demand at Node 1.  Describe in detail the interpretation of the value in Cell I10.


Question 3 (4Points):  There are two constraints in this problem:  first is the relationship between the Net Flow and Supply/Demand.  Describe this relationship and then incorporate the constraint in RSPE.
Constraint:


Question 4 (4 Points):  The second constraint is the relationship between the Flow (decision variables) and the minimum number of units that must be moved from each node.  Describe this relationship and then incorporate the constraint in RSPE.
Flow ($B6:$B16) >= Min ($A$6:$A$14)

Question 5 (4 Points):  The formula for the Objective Function in Cell E16 is missing.  Enter the appropriate formula and describe what is being calculated in that cell.  Once you have entered the formula and the two constraints from Questions 3 and 4 above, solve the model.  What is the optimal solution?
,36321;'452/582
152., 6ilujyk,./On the tab labeled "Network Diagram", I have provided a visual representation of the network for Problem #9 on Page 227.   On the tab labeled "Production Plan," you will see the integration of the general framework of the network integrated into Excel.    Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

Proceed to the Solutions tab where you will find five questions.  To answer each question, you will be required to consult the Network Diagram, enter values into the spreadsheet and then transfer some information to ASPE.  In your response to each question, start by entering the appropriate information into the spreadsheet or ASPE and then answer the remainder of the question in a written response.  Each question is worth 4 points:  2 points for making the correct inputs to the spreadsheet or ASPE and 2 points for a clear, concise, grammatically
Good luck, enjoy the collaboration with your teammate and as always...HAVE FUN! '

1[- t.ky\9ohls,dflghbn. ;/tion 1 (4 Points):  In the Column labeled "To" (Column D), fill in the numbers of the appropriate nodes based on your review of the network diagram.  The Cost information in the model should be helpful in filling out this column.  Describe what the "To" nodes represent in the model.  

Question 2 (4 Points): In the Column labeled "Supply/Demand" (Column I), fill in the  appropriate Supply (should be typed as a negative number) or Demand (should be typed in as a positive number) for the respective node.  For example, Cell I6 would be the supply or demand at Node 1.  Describe in detail the interpretation of the value in Cell I10.


Question 3 (4Points):  There are two constraints in this problem:  first is the relationship between the Net Flow and Supply/Demand.  Describe this relationship and then incorporate the constraint in RSPE.
Constraint:


Question 4 (4 Points):  The second constraint is the relationship between the Flow (decision variables) and the minimum number of units that must be moved from each node.  Describe this relationship and then incorporate the constraint in RSPE.
Flow ($B6:$B16) >= Min ($A$6:$A$14)

Question 5 (4 Points):  The formula for the Objective Function in Cell E16 is missing.  Enter the appropriate formula and describe what is being calculated in that cell.  Once you have entered the formula and the two constraints from Questions 3 and 4 above, solve the model.  What is the optimal solution?
,36321;'452/582
152., 6ilujyk,./On the tab labeled "Network Diagram", I have provided a visual representation of the network for Problem #9 on Page 227.   On the tab labeled "Production Plan," you will see the integration of the general framework of the network integrated into Excel.    Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

Proceed to the Solutions tab where you will find five questions.  To answer each question, you will be required to consult the Network Diagram, enter values into the spreadsheet and then transfer some information to ASPE.  In your response to each question, start by entering the appropriate information into the spreadsheet or ASPE and then answer the remainder of the question in a written response.  Each question is worth 4 points:  2 points for making the correct inputs to the spreadsheet or ASPE and 2 points for a clear, concise, grammatically
Good luck, enjoy the collaboration with your teammate and as always...HAVE FUN! '

1[- t.ky\9ohls,dflghbn. ;/tion 1 (4 Points):  In the Column labeled "To" (Column D), fill in the numbers of the appropriate nodes based on your review of the network diagram.  The Cost information in the model should be helpful in filling out this column.  Describe what the "To" nodes represent in the model.  

Question 2 (4 Points): In the Column labeled "Supply/Demand" (Column I), fill in the  appropriate Supply (should be typed as a negative number) or Demand (should be typed in as a positive number) for the respective node.  For example, Cell I6 would be the supply or demand at Node 1.  Describe in detail the interpretation of the value in Cell I10.


Question 3 (4Points):  There are two constraints in this problem:  first is the relationship between the Net Flow and Supply/Demand.  Describe this relationship and then incorporate the constraint in RSPE.
Constraint:


Question 4 (4 Points):  The second constraint is the relationship between the Flow (decision variables) and the minimum number of units that must be moved from each node.  Describe this relationship and then incorporate the constraint in RSPE.
Flow ($B6:$B16) >= Min ($A$6:$A$14)

Question 5 (4 Points):  The formula for the Objective Function in Cell E16 is missing.  Enter the appropriate formula and describe what is being calculated in that cell.  Once you have entered the formula and the two constraints from Questions 3 and 4 above, solve the model.  What is the optimal solution?
,36321;'452/582
152., 6ilujyk,./On the tab labeled "Network Diagram", I have provided a visual representation of the network for Problem #9 on Page 227.   On the tab labeled "Production Plan," you will see the integration of the general framework of the network integrated into Excel.    Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

Proceed to the Solutions tab where you will find five questions.  To answer each question, you will be required to consult the Network Diagram, enter values into the spreadsheet and then transfer some information to ASPE.  In your response to each question, start by entering the appropriate information into the spreadsheet or ASPE and then answer the remainder of the question in a written response.  Each question is worth 4 points:  2 points for making the correct inputs to the spreadsheet or ASPE and 2 points for a clear, concise, grammatically
Good luck, enjoy the collaboration with your teammate and as always...HAVE FUN! '

1[- t.ky\9ohls,dflghbn. ;/tion 1 (4 Points):  In the Column labeled "To" (Column D), fill in the numbers of the appropriate nodes based on your review of the network diagram.  The Cost information in the model should be helpful in filling out this column.  Describe what the "To" nodes represent in the model.  

Question 2 (4 Points): In the Column labeled "Supply/Demand" (Column I), fill in the  appropriate Supply (should be typed as a negative number) or Demand (should be typed in as a positive number) for the respective node.  For example, Cell I6 would be the supply or demand at Node 1.  Describe in detail the interpretation of the value in Cell I10.


Question 3 (4Points):  There are two constraints in this problem:  first is the relationship between the Net Flow and Supply/Demand.  Describe this relationship and then incorporate the constraint in RSPE.
Constraint:


Question 4 (4 Points):  The second constraint is the relationship between the Flow (decision variables) and the minimum number of units that must be moved from each node.  Describe this relationship and then incorporate the constraint in RSPE.
Flow ($B6:$B16) >= Min ($A$6:$A$14)

Question 5 (4 Points):  The formula for the Objective Function in Cell E16 is missing.  Enter the appropriate formula and describe what is being calculated in that cell.  Once you have entered the formula and the two constraints from Questions 3 and 4 above, solve the model.  What is the optimal solution?
,36321;'452/582
152., 6ilujyk,./s tab where you will find five questions.  To answer each question, you will be required to consult the Network Diagram, enter values into the spreadsheet and then transfer some information to ASPE.  In your response to each question, start by entering the appropriate information into the spreadsheet or ASPE and then answer the remainder of the question in a written response.  Each question is worth 4 points:  2 points for making the correct inputs to the spreadsheet or ASPE and 2 points for a clear, concise, grammatically
Good luck, enjoy the collaboration with your teammate and as always...HAVE FUN! '

1[- t.ky\9ohls,dflghbn. ;/tion 1 (4 Points):  In the Column labeled "To" (Column D), fill in the numbers of the appropriate nodes based on your review of the network diagram.  The Cost information in the model should be helpful in filling out this column.  Describe what the "To" nodes represent in the model.  

Question 2 (4 Points): In the Column labeled "Supply/Demand" (Column I), fill in the  appropriate Supply (should be typed as a negative number) or Demand (should be typed in as a positive number) for the respective node.  For example, Cell I6 would be the supply or demand at Node 1.  Describe in detail the interpretation of the value in Cell I10.


Question 3 (4Points):  There are two constraints in this problem:  first is the relationship between the Net Flow and Supply/Demand.  Describe this relationship and then incorporate the constraint in RSPE.
Constraint:


Question 4 (4 Points):  The second constraint is the relationship between the Flow (decision variables) and the minimum number of units that must be moved from each node.  Describe this relationship and then incorporate the constraint in RSPE.
Flow ($B6:$B16) >= Min ($A$6:$A$14)

Question 5 (4 Points):  The formula for the Objective Function in Cell E16 is missing.  Enter the appropriate formula and describe what is being calculated in that cell.  Once you have entered the formula and the two constraints from Questions 3 and 4 above, solve the model.  What is the optimal solution?
,

BUSI508 Week 3 Chapter 4, Page 184, Case 4.2 SCORE 100 PERCENT

On the tab labeled "Original Problem", I have provided the modeling of Case 4.2 beginning on Page 184.  Carefully read the case in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

On the "Original Problem" tab, there are five questions.  After loading the Excel Solver, solve the model, obtain the sensitivity report, and use the sensitivity report to answer Questions 1 though 5.  Each question is worth 16 points:  8 points for correctly identifying the cell value(s) you used from the sensitivity report to justify your response and 8 points for a clear, concise, grammatically response correctly answering the question. Your responses should be typed in unbolded black font right after the statement of each question.  

Remember, cases are individual work.  Good luck and as always...HAVE FUN!

Question 1 (16 Points):  What is the optimal solution and associated profit?

Question 2 (16 Points):  A local distributor has offered to sell Parket Sisters an additional 500 ounces of stainless steel for sixty cents per ounce more than it ordinarily pays.  Should the company buy the steel at that price?  Explain your answer.

Question 3 (16 Points):  Parket Sisters has an opportunity to sell some of its plastic for $6.50 per ounce to another company.  The other company (which does not produce pens or pencils and therefore is not a competitor) wants to buy 300 ounces of plastic.  Should Parket Sisters sell the plastic to the other company?  What happens to Parket Sisters' product mix and overall profit if it does sell the plastic.  Be as specific as possible.


Question 4 (16 Points):  The R&D Department at Parket Sisters has been redesigning the mechanical pencil to make it more profitable.  The new design requires 1.1 ounce of plastic, 2.0 ounces of chrome, and 2.0 ounces of stainless steel.  If the company can sell one of these new pencils at a net profit of $3.00, should it approve the new design?  Explain your response.
Yes, this new desihn should be approved as wih new design company can produce pencil an increase total profit to $2,800.

Question 5 (16 Points):  If the profit on a fountain pen is $6.75 instead of $5.00, what is the optimal product mix and optimal profit?

  

BUSI508 Week 3 Chapter 4 Peoblem 17 SCORE 100 PERCENT

On the tab labeled "Original Problem", I have provided the modeling of Problem #18 on Page 119 in Chapter 3 with some minor modifications.  Carefully read the statement of the problem in the textbook and then review the model to familiarize yourself with the integration of the LP into Excel.  

Your first requirement is to load the solver based on the set up I have provided on the Original Problem tab assuming you want to minimize the cost of producing a mix that meets the constraints noted in the textbook.  In loading the solver, there is no need to change any cell values or equations in the spreadsheet itself.  As a hint, the cells highlighted in YELLOW are either decision variables, or the optimization cell.  Once you have loaded the solver and solved the problem, you are required to obtain the sensitivity analysis; if you do this correctly, the analysis will show up in a new tab in the bottom left-hand corner of the sheet.  If you are unsure how to obtain the report, please review my video in the Content area.  HINT:  if you have loaded the solver correctly, the minimized cost should be between $5.25 and $5.35.

From there, proceed to the "Solutions" tab where you will find five questions.  To answer each question, you will be required to consult the sensitivity analysis and locate the correct information from the analysis to answer each question.  All answers should come from solving the model (after loading the solver) and obtaining and consulting the sensitivity data, not by resolving the model multiple times!

In your response to each question, you should begin with a written sentence(s) that explains where specifically in the sensitivity analysis you found the information you need to answer each question followed by a sentence answering each respective question.  Each question is worth 4 points:  2 points for explaining where in the sensitivity analysis you found the information necessary to answer the question (mechanical component) and 2 points for a clear, concise, grammatically answer to the question (written component).  Questions should be answered on the Solutions tab and typed in unbolded print right after the statement of the question.  

Good luck, and as always...HAVE FUN!

1 (4 Points):  What is the optimal solution?

2. (4 Points):  What would happen to the optimal solution if the cost per pound of grain decreaed by five cents?

3. (4 Points):  What would happen to the optimal solution if the cost per pound of chocolate increased by eighteen cents?

4.  (4 Points):  Considering the four nutritional constraints (vitamins, minerals, protein, and calories), explain why the shadow prices of protein and calories are zero and the shadow prices of vitamins and minerals are non-zero.


5. (4 Points):  In the Contstaints portion of the sensitivity analysis, use the shadow price for "Amount (lbs) Total" to determine the total cost of the mix if the amount of mix increased from 2 to 2.02 pounds.

 

BUSI508 Week 2 Assignment Chapter 3, Pages 138, Case 3.4 SCORE 100 PERCENT

Incorporate the five changes noted below and solve the problem only after you have done so!  None of the changes noted below impact the cells in Rows 18, 19, or 20.  I have not provided any hints, however, this Case study requires some of the same strategies we used to solve the Excel Exercise.  Good luck and if you have any questions, please post them on the discussion board so that everyone has access to the same information!!  Thanks.

1.  (16 Points) Tom now wants to run full-page ads in both major newspapers for at least two weeks leading up to the vote.  NOTE:  this changes the minimum value in two cells in Column C as we are assuming this applies to both daily and Sunday newspapers.


2.  (16 Points) Tom is scaling back his daytime television advertising strategy which will now consist of running at least two but no more than four spots per week for the four weeks leading up to the vote.


3.  (16 Points) Tom wants to derive at least 10% of his total advertising impact from evening television advertisements.


4.  (16 Points) Tom has decided he is willing to run a maximum of 6, 15-second radio spots per day for the 28 days leading up to the vote and a maximum of 7, 30-second spots per day over the same period of time.   However, he wants to ensure the total impact derived from radio does not exceed 65% of the total impact.  

5.  (16 Points) With his increase in radio spots, Tom plans to use the majority of these new spots in the Orlando, Tampa, and Miami markets thus he feels the billboards in these cities are no longer required for advertisement.  However, because Tom feels there is value in billboard advertising, he wants to derive at least 1% of his total impact from billboards.

BUSI508 Week 1 Discussion 1 SCORE 100 PERCENT

The Dreaded "M" word...Math

Many students entering BUSI 508 are apprehensive about the course because they know there is a math component to the course.  If a fellow classmate told you he/she was apprehensive about the course, what would you tell him/her in order to overcome any fears and be successful in the course?

BUSI508 Midterm Exam SCORE 99 PERCENT

Quiz
Question 1 (1 point)
 
The specification or description of the relationship between the dependent and independent variables is generally called
Question 1 options:


a)

 
a constraint.


b)
a declaration.


c)
a function.


d)
a mathematical model.
Question 2 (1 point)
 
The ultimate goal of the problem identification step of the problem-solving process is
Question 2 options:


a)
collecting lots of information.


b)
helping the decision maker realize there is a problem.


c)
identifying the root problem or problems causing the mess.


d)
convincing the decision maker the mess is really a problem that can be solved.
Question 3 (1 point)
 
To be effective, a modeler must
Question 3 options:


a)
be an effective presenter of results.


b)
collect the proper input data for the model.


c)
understand how modeling fits into the problem-solving process.


d)
apply the correct modeling technique.
Question 4 (1 point)
 
The goal of the modeling approach to problem solving is to
Question 4 options:


a)
help individuals make good decisions.


b)
ensure optimality of decisions.


c)
determine a set of optimal decisions.


d)
determine feasibility of decisions.
Question 5 (1 point)
 
A mathematical model is considered to be "valid" when
Question 5 options:


a)
it accurately represents the relevant characteristics of the object or decision.


b)
it has passed a validation test.


c)
it replicates all aspects of the object or decision.


d)
the left-hand and right-hand sides of expressions are equal.
Question 6 (1 point)
 
Variables are termed independent when they satisfy which of the following?
Question 6 options:


a)
The function value depends upon their values.


b)
The decision maker has no control over them.


c)
The variables have no relationship to one another.


d)
The variable is described as an output of the spreadsheet model.
Question 7 (1 point)
 
The best models
Question 7 options:


a)
accurately reflect relevant characteristics of the real-world object or decision.


b)
are mathematical models.


c)
replicate all aspects of the real-world object or decision.


d)
replicate the characteristics of a component in isolation from the rest of the system.
Question 8 (1 point)
 
In which of the following categories of modeling techniques do the independent variables have unknown or uncertain values or coefficients?
Question 8 options:


a)
Descriptive models


b)
Predictive models


c)
Prescriptive models


d)
Probabilistic models
Question 9 (1 point)
 
Which of the following fields of study is defined in Chapter One as the one that "uses computers, statistics, and mathematics to solve business problems"?
Question 9 options:


a)
Accounting


b)
Information systems


c)
Business analytics


d)
Scientific management
Question 10 (1 point)
 
Solutions to which of the following categories of modeling techniques indicate a course of action to the decision maker?
Question 10 options:


a)
Descriptive models


b)
Predictive models


c)
Prescriptive models


d)
Preventive models
Question 11 (1 point)
 
Which of the following statements is true of using models in problem solving and decision analysis?
Question 11 options:


a)
It is a fairly new idea.


b)
It is required in order to find good solutions.


c)
It is something everyone has done before.


d)
It is tied to the use of computers.
Question 12 (1 point)
 
Why would someone wish to use a spreadsheet model?
Question 12 options:


a)
To implement a computer model.


b)
Because spreadsheets are convenient.


c)
To analyze decision alternatives.


d)
All of these.
Question 13 (1 point)
 
A company makes two products, X1 and X2. They require at least 20 of each be produced. Which set of lower bound constraints reflect this requirement?
Question 13 options:


a)
X1 ≥ 20, X2 ≥ 20


b)
X1 + X2 ≥ 20


c)
X1 + X2 ≥ 40


d)
X1 ≥ 20, X2 ≥ 20, X1 + X2 ≤ 40
Question 14 (1 point)
 
A diet is being developed which must contain at least 100 mg of vitamin C. Two fruits are used in this diet. Bananas contain 30 mg of vitamin C and Apples contain 20 mg of vitamin C. The diet must contain at least 100 mg of vitamin C. Which of the following constraints reflects the relationship between Bananas, Apples and vitamin C?
Question 14 options:


a)
20 A + 30 B ≥ 100


b)
20 A + 30 B ≤ 100


c)
20 A + 30 B = 100


d)
20 A = 100
Question 15 (1 point)
 
A company uses 4 pounds of resource 1 to make each unit of X1 and 3 pounds of resource 1 to make each unit of X2. There are only 150 pounds of resource 1 available. Which of the following constraints reflects the relationship between X1, X2 and resource 1?
Question 15 options:


a)
4 X1 + 3 X2 ≥ 150


b)
4 X1 + 3 X2 ≤ 150


c)
4 X1 + 3 X2 = 150


d)
4 X1 ≤ 150
Question 16 (1 point)
 
The desire to maximize profits is an example of a(n)
Question 16 options:


a)
decision.


b)
constraint.


c)
objective.


d)
parameter.
Question 17 (1 point)
 
The first step in formulating a linear programming problem is
Question 17 options:


a)
Identify any upper or lower bounds on the decision variables.


b)
State the constraints as linear combinations of the decision variables.


c)
Understand the problem.


d)
Identify the decision variables.


e)
State the objective function as a linear combination of the decision variables.
Question 18 (1 point)
 
The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits.

X1 = number of product 1 produced in each batch
X2 = number of product 2 produced in each batch

MAX: 150 X1 + 250 X2
Subject to: 2 X1 + 5 X2 ≤ 200
  3 X1 + 7 X2 ≤ 175
  X1, X2 ≥ 0


How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?
Question 18 options:


a)
750


b)
2500


c)
2750


d)
3250
Question 19 (1 point)
 
The constraint for resource 1 is 5 X1 + 4 X2 ≥ 200. If X1 = 40 and X2 = 20, how many additional units, if any, of resource 1 are employed above the minimum of 200?
Question 19 options:


a)
0


b)
20


c)
40


d)
80
Question 20 (1 point)
 
Which of the following actions would expand the feasible region of an LP model?
Question 20 options:


a)
Loosening the constraints.


b)
Tightening the constraints.


c)
Multiplying each constraint by 2.


d)
Adding an additional constraint.
Question 21 (1 point)
 
A common objective in the product mix problem is
Question 21 options:


a)
maximizing cost.


b)
maximizing profit.


c)
minimizing production time.


d)
maximizing production volume.
Question 22 (1 point)
 
The objective function for a LP model is 3 X1 + 2 X2. If X1 = 20 and X2 = 30, what is the value of the objective function?
Question 22 options:


a)
0


b)
50


c)
60


d)
120
Question 23 (1 point)
 
What is the goal in optimization?
Question 23 options:


a)
Find the decision variable values that result in the best objective function and satisfy all constraints.


b)
Find the values of the decision variables that use all available resources.


c)
Find the values of the decision variables that satisfy all constraints.


d)
None of these.
Question 24 (1 point)
 
Linear programming problems have
Question 24 options:


a)
linear objective functions, non-linear constraints.


b)
non-linear objective functions, non-linear constraints.


c)
non-linear objective functions, linear constraints.


d)
linear objective functions, linear constraints.
Question 25 (1 point)
 
Which type of spreadsheet cell represents the left hand sides (LHS) formulas in an LP model?
Question 25 options:


a)
Target or set cell


b)
Changing variable cell


c)
Constraint cell


d)
Constant cell
Question 26 (1 point)
 
Which type of spreadsheet cell represents the objective function in an LP model?
Question 26 options:


a)
Objective cell


b)
Changing variable cell


c)
Constraint cell


d)
Constant cell
Question 27 (1 point)
 
Which type of spreadsheet cell represents the decision variables in an LP model?
Question 27 options:


a)
Target or set cell


b)
Variable cell


c)
Constraint cell


d)
Constant cell
Question 28 (1 point)
 
The constraints X1 ≥ 0 and X2 ≥ 0 are referred to as
Question 28 options:


a)
positivity constraints.


b)
optimality conditions.


c)
left hand sides.


d)
nonnegativity conditions.
Question 29 (2 points)
 

Exhibit 3.1

The following questions are based on this problem and accompanying Excel windows.

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.

 
Let X1 = Number of Beds to produce
  X2 = Number of Desks to produce


The LP model for the problem is

 
MAX: 30 X1 + 40 X2
Subject to: 6 X1 + 4 X2 ≤ 36 (carpentry)
  4 X1 + 8 X2 ≤ 40 (varnishing)
  X2 ≤ 8 (demand for desks)
  X1, X2 ≥ 0

 
  A B C D E
1 Jones Furniture
2
3 Beds Desks
4 Number to make: Total Profit:
5 Unit profit: 30 40
6
7 Constraints: Used Available
8 Carpentry 6 4 36
9 Varnishing 4 8 40
10 Desk demand 1 8

 

Refer to Exhibit 3.1. What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total profit?

Question 29 options:


a)


=B4*B5+C4*C5


b)


=SUMPRODUCT(B8:C8,$B$4:$C$4)


c)


=SUM(B5:C5)


d)


=SUM(E8:E10)
Question 30 (2 points)
 

Exhibit 3.1

The following questions are based on this problem and accompanying Excel windows.

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.

 
Let X1 = Number of Beds to produce
  X2 = Number of Desks to produce


The LP model for the problem is

 
MAX: 30 X1 + 40 X2
Subject to: 6 X1 + 4 X2 ≤ 36 (carpentry)
  4 X1 + 8 X2 ≤ 40 (varnishing)
  X2 ≤ 8 (demand for desks)
  X1, X2 ≥ 0

 
  A B C D E
1 Jones Furniture
2
3 Beds Desks
4 Number to make: Total Profit:
5 Unit profit: 30 40
6
7 Constraints: Used Available
8 Carpentry 6 4 36
9 Varnishing 4 8 40
10 Desk demand 1 8

 

Refer to Exhibit 3.1. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of carpentry used?

Question 30 options:


a)


=B4*B5+C4*C5


b)


=SUMPRODUCT(B8:C8,$B$4:$C$4)


c)


=SUM(B5:C5)


d)


=SUM(E8:E10)
Question 31 (2 points)
 

Exhibit 3.1

The following questions are based on this problem and accompanying Excel windows.

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.

 
Let X1 = Number of Beds to produce
  X2 = Number of Desks to produce


The LP model for the problem is

 
MAX: 30 X1 + 40 X2
Subject to: 6 X1 + 4 X2 ≤ 36 (carpentry)
  4 X1 + 8 X2 ≤ 40 (varnishing)
  X2 ≤ 8 (demand for desks)
  X1, X2 ≥ 0

 
  A B C D E
1 Jones Furniture
2
3 Beds Desks
4 Number to make: Total Profit:
5 Unit profit: 30 40
6
7 Constraints: Used Available
8 Carpentry 6 4 36
9 Varnishing 4 8 40
10 Desk demand 1 8

 

Refer to Exhibit 3.1. Which cells should be changing cells in this problem?

Question 31 options:


a)


B4:C4


b)


E5


c)


D8:D10


d)


E8:E10
Question 32 (2 points)
 

Exhibit 3.1

The following questions are based on this problem and accompanying Excel windows.

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.

 
Let X1 = Number of Beds to produce
  X2 = Number of Desks to produce


The LP model for the problem is

 
MAX: 30 X1 + 40 X2
Subject to: 6 X1 + 4 X2 ≤ 36 (carpentry)
  4 X1 + 8 X2 ≤ 40 (varnishing)
  X2 ≤ 8 (demand for desks)
  X1, X2 ≥ 0

 
  A B C D E
1 Jones Furniture
2
3 Beds Desks
4 Number to make: Total Profit:
5 Unit profit: 30 40
6
7 Constraints: Used Available
8 Carpentry 6 4 36
9 Varnishing 4 8 40
10 Desk demand 1 8

 

Refer to Exhibit 3.1. Which of the following statements represent the carpentry, varnishing and limited demand for desks constraints?

Question 32 options:


a)


B4:C4 ≤ B5:C5


b)


E5 ≤ 0


c)


D8:D10 ≤ E8:E10


d)


E8:E10 ≤ D8:D10
Question 33 (1 point)
 
Given an objective function value of 150 and a shadow price for resource 1 of 5, if 10 more units of resource 1 are added (assuming the allowable increase is greater than 10), what is the impact on the objective function value?
Question 33 options:


a)
increase of 50


b)
increase of unknown amount


c)
decrease of 50


d)
increase of 10
Question 34 (1 point)
 
Which of the following statements is false concerning either of the Allowable Increase and Allowable Decrease columns in the Sensitivity Report?
Question 34 options:


a)
The values equate the decision variable profit to the cost of resources expended.


b)
The values give the range over which a shadow price is accurate.


c)
The values give the range over which an objective function coefficient can change without changing the optimal solution.


d)
The values provide a means to recognize when alternate optimal solution exist.
Question 35 (1 point)
 
A binding less than or equal to (≤) constraint in a maximization problem means
Question 35 options:


a)
that all of the resource represented by the constraint is consumed in the solution.


b)
it is not a constraint that the level curve contacts.


c)
another constraint is limiting the solution.


d)
the requirement for the constraint has been exceeded.
Question 36 (1 point)
 
The allowable decrease for a changing cell (decision variable) is
Question 36 options:


a)
the amount by which the constraint coefficient can decrease without changing final optimal solution.


b)
an indication of how many more units to produce to maximize profits.


c)
the amount by which objective function coefficient can decrease without changing the final optimal solution.


d)
an indication of how much to charge to get the optimal solution.
Question 37 (1 point)
 
The allowable increase for a constraint is
Question 37 options:


a)
how many more units of resource to purchase to maximize profits.


b)
the amount by which the resource can increase given shadow price.


c)
how much resource to use to get the optimal solution.


d)
the amount by which the constraint coefficient can increase without changing the final optimal value.
Question 38 (1 point)
 
A binding greater than or equal to (≥) constraint in a minimization problem means that
Question 38 options:


a)
the variable is up against an upper limit.


b)
the minimum requirement for the constraint has just been met.


c)
another constraint is limiting the solution.


d)
the shadow price for the constraint will be positive.
Question 39 (1 point)
 
The allowable increase for a changing cell (decision variable) is
Question 39 options:


a)
how many more units to produce to maximize profits.


b)
the amount by which the objective function coefficient can increase without changing the optimal solution.


c)
how much to charge to get the optimal solution.


d)
the amount by which constraint coefficient can increase without changing the optimal solution.
Question 40 (1 point)
 
If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?
Question 40 options:


a)
increase of 100


b)
increase of 110


c)
decrease of 100


d)
increases but by unknown amount
Question 41 (2 points)
 

Exhibit 4.1

The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report.

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):

 

Week


Trucking Limits


Railway Limits


Air Cargo Limits

1


45


60


15

2


50


55


10

3


55


45


5

Costs ($ per 1000 tons)


$200


$140


$400


The following is the LP model for this logistics problem.

 
Let Xij = amount shipped by mode i in week j
  where i = 1(Truck), 2(Rail), 3(Air)
  and j = 1, 2, 3
 
Let WLij = weekly limit of mode i in week j (as provided in above table)
 
MIN: 200(X11 + X12 + X13) + 140(X21 + X22 + X23) + 500(X31 + X32 + X33)
Subject to:
Xij ≤ WL ij for all i and j Weekly limits by mode
X11 + X12 + X13 + X21 + X22 + X23 + X31 + X32 + X33 ≥ 250 Total at end of three weeks
X11 + X21 + X31 + X12 + X22 + X32 ≥ 200 Total at end of two weeks
X11 + X21 + X31 ≥ 120 Total at end of first week
X11 + X12 + X13 ≥ 0.45*250 Truck mix requirement
X21 + X22 + X23 ≥ 0.40*250 Rail mix requirement
X31 + X32 + X33 ≤ 0.15*250 Air mix limit
Xij ≥ 0 for all i and j


 
 

Final


Reduced


Objective


Allowable


Allowable
Cell Name

Value


Cost


Coefficient


Increase


Decrease
$D$6 Week 1 by Truck

45


0


200


360


1E+30
$E$6 Week 1 by Rail

60


0


140


360


1E+30
$F$6 Week 1 by Air

15


0


500


1E+30


360
$D$7 Week 2 by Truck

50


0


200


0


1E+30
$E$7 Week 2 by Rail

55


0


140


0


1E+30
$F$7 Week 2 by Air

0


360


500


1E+30


360
$D$8 Week 3 by Truck

13


0


200


1E+30


0
$E$8 Week 3 by Rail

12


0


140


60


0
$F$8 Week 3 by Air

0


360


500


1E+30


360
 
Constraints
 

Final


Shadow


Constraint


Allowable


Allowable
Cell Name

Value


Price


R.H. Side


Increase


Decrease
$D$18 Week 1 by Truck

45


−360


45


13


0
$E$18 Week 1 by Rail

60


−360


60


15


0
$F$18 Week 1 by Air

15


0


15


1E+30


0
$D$19 Week 2 by Truck

50


0


50


13


25
$E$19 Week 2 by Rail

55


0


55


12


25
$F$19 Week 2 by Air

0


0


10


1E+30


10
$D$20 Week 3 by Truck

13


0


55


1E+30


42
$E$20 Week 3 by Rail

12


0


45


1E+30


33
$F$20 Week 3 by Air

0


0


5


1E+30


5
$D$9 Shipped by Truck

108


60


108


12


13
$E$9 Shipped by Rail

127


0


100


27


1E+30
$F$13 Total Shipped Tons

250


140


250


33


0
$F$9 Shipped by Air

15


0


37.5


1E+30


22.5
$G$6 Week 1 Totals

120


360


120


0


15
$G$7 Week 2 Totals

225


0


200


25


1E+30
$G$8 Week 3 Totals

250


0


250


0


1E+30

Refer to Exhibit 4.1. The Week 1 by Truck and Week 1 by Rail constraints each have a shadow price of −360. What do these values imply?
These values imply that increasing the weekly limits on these two modes will reduce total cost by $360 per unit increase in limit.
Question 41 options:
Question 42 (2 points)
 

Exhibit 4.1

The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report.

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):

 

Week


Trucking Limits


Railway Limits


Air Cargo Limits

1


45


60


15

2


50


55


10

3


55


45


5

Costs ($ per 1000 tons)


$200


$140


$400


The following is the LP model for this logistics problem.

 
Let Xij = amount shipped by mode i in week j
  where i = 1(Truck), 2(Rail), 3(Air)
  and j = 1, 2, 3
 
Let WLij = weekly limit of mode i in week j (as provided in above table)
 
MIN: 200(X11 + X12 + X13) + 140(X21 + X22 + X23) + 500(X31 + X32 + X33)
Subject to:
Xij ≤ WL ij for all i and j Weekly limits by mode
X11 + X12 + X13 + X21 + X22 + X23 + X31 + X32 + X33 ≥ 250 Total at end of three weeks
X11 + X21 + X31 + X12 + X22 + X32 ≥ 200 Total at end of two weeks
X11 + X21 + X31 ≥ 120 Total at end of first week
X11 + X12 + X13 ≥ 0.45*250 Truck mix requirement
X21 + X22 + X23 ≥ 0.40*250 Rail mix requirement
X31 + X32 + X33 ≤ 0.15*250 Air mix limit
Xij ≥ 0 for all i and j


 
 

Final


Reduced


Objective


Allowable


Allowable
Cell Name

Value


Cost


Coefficient


Increase


Decrease
$D$6 Week 1 by Truck

45


0


200


360


1E+30
$E$6 Week 1 by Rail

60


0


140


360


1E+30
$F$6 Week 1 by Air

15


0


500


1E+30


360
$D$7 Week 2 by Truck

50


0


200


0


1E+30
$E$7 Week 2 by Rail

55


0


140


0


1E+30
$F$7 Week 2 by Air

0


360


500


1E+30


360
$D$8 Week 3 by Truck

13


0


200


1E+30


0
$E$8 Week 3 by Rail

12


0


140


60


0
$F$8 Week 3 by Air

0


360


500


1E+30


360
 
Constraints
 

Final


Shadow


Constraint


Allowable


Allowable
Cell Name

Value


Price


R.H. Side


Increase


Decrease
$D$18 Week 1 by Truck

45


−360


45


13


0
$E$18 Week 1 by Rail

60


−360


60


15


0
$F$18 Week 1 by Air

15


0


15


1E+30


0
$D$19 Week 2 by Truck

50


0


50


13


25
$E$19 Week 2 by Rail

55


0


55


12


25
$F$19 Week 2 by Air

0


0


10


1E+30


10
$D$20 Week 3 by Truck

13


0


55


1E+30


42
$E$20 Week 3 by Rail

12


0


45


1E+30


33
$F$20 Week 3 by Air

0


0


5


1E+30


5
$D$9 Shipped by Truck

108


60


108


12


13
$E$9 Shipped by Rail

127


0


100


27


1E+30
$F$13 Total Shipped Tons

250


140


250


33


0
$F$9 Shipped by Air

15


0


37.5


1E+30


22.5
$G$6 Week 1 Totals

120


360


120


0


15
$G$7 Week 2 Totals

225


0


200


25


1E+30
$G$8 Week 3 Totals

250


0


250


0


1E+30

Refer to Exhibit 4.1. Of the three percentage of effort constraints, Shipped by Truck, Shipped by Rail, and Shipped by Air, which should be examined for potential cost reduction?

In this case, the percentage by Truck, Shipped by Truck, should be examined. Decreasing the percentage by truck will decrease cost as the shadow price is 60.
Question 43 (2 points)
 

Exhibit 4.1

The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report.

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):

 

Week


Trucking Limits


Railway Limits


Air Cargo Limits

1


45


60


15

2


50


55


10

3


55


45


5

Costs ($ per 1000 tons)


$200


$140


$400


The following is the LP model for this logistics problem.

 
Let Xij = amount shipped by mode i in week j
  where i = 1(Truck), 2(Rail), 3(Air)
  and j = 1, 2, 3
 
Let WLij = weekly limit of mode i in week j (as provided in above table)
 
MIN: 200(X11 + X12 + X13) + 140(X21 + X22 + X23) + 500(X31 + X32 + X33)
Subject to:
Xij ≤ WL ij for all i and j Weekly limits by mode
X11 + X12 + X13 + X21 + X22 + X23 + X31 + X32 + X33 ≥ 250 Total at end of three weeks
X11 + X21 + X31 + X12 + X22 + X32 ≥ 200 Total at end of two weeks
X11 + X21 + X31 ≥ 120 Total at end of first week
X11 + X12 + X13 ≥ 0.45*250 Truck mix requirement
X21 + X22 + X23 ≥ 0.40*250 Rail mix requirement
X31 + X32 + X33 ≤ 0.15*250 Air mix limit
Xij ≥ 0 for all i and j


 
 

Final


Reduced


Objective


Allowable


Allowable
Cell Name

Value


Cost


Coefficient


Increase


Decrease
$D$6 Week 1 by Truck

45


0


200


360


1E+30
$E$6 Week 1 by Rail

60


0


140


360


1E+30
$F$6 Week 1 by Air

15


0


500


1E+30


360
$D$7 Week 2 by Truck

50


0


200


0


1E+30
$E$7 Week 2 by Rail

55


0


140


0


1E+30
$F$7 Week 2 by Air

0


360


500


1E+30


360
$D$8 Week 3 by Truck

13


0


200


1E+30


0
$E$8 Week 3 by Rail

12


0


140


60


0
$F$8 Week 3 by Air

0


360


500


1E+30


360
 
Constraints
 

Final


Shadow


Constraint


Allowable


Allowable
Cell Name

Value


Price


R.H. Side


Increase


Decrease
$D$18 Week 1 by Truck

45


−360


45


13


0
$E$18 Week 1 by Rail

60


−360


60


15


0
$F$18 Week 1 by Air

15


0


15


1E+30


0
$D$19 Week 2 by Truck

50


0


50


13


25
$E$19 Week 2 by Rail

55


0


55


12


25
$F$19 Week 2 by Air

0


0


10


1E+30


10
$D$20 Week 3 by Truck

13


0


55


1E+30


42
$E$20 Week 3 by Rail

12


0


45


1E+30


33
$F$20 Week 3 by Air

0


0


5


1E+30


5
$D$9 Shipped by Truck

108


60


108


12


13
$E$9 Shipped by Rail

127


0


100


27


1E+30
$F$13 Total Shipped Tons

250


140


250


33


0
$F$9 Shipped by Air

15


0


37.5


1E+30


22.5
$G$6 Week 1 Totals

120


360


120


0


15
$G$7 Week 2 Totals

225


0


200


25


1E+30
$G$8 Week 3 Totals

250


0


250


0


1E+30

Refer to Exhibit 4.1. Are there alternate optimal solutions to this problem?
It is not possible to tell if there are alternate optimal solutions to this problem as e cannot rule out Degeneracy.
Question 44 (2 points)
 

Exhibit 4.1

The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report.

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):

 

Week


Trucking Limits


Railway Limits


Air Cargo Limits

1


45


60


15

2


50


55


10

3


55


45


5

Costs ($ per 1000 tons)


$200


$140


$400


The following is the LP model for this logistics problem.

 
Let Xij = amount shipped by mode i in week j
  where i = 1(Truck), 2(Rail), 3(Air)
  and j = 1, 2, 3
 
Let WLij = weekly limit of mode i in week j (as provided in above table)
 
MIN: 200(X11 + X12 + X13) + 140(X21 + X22 + X23) + 500(X31 + X32 + X33)
Subject to:
Xij ≤ WL ij for all i and j Weekly limits by mode
X11 + X12 + X13 + X21 + X22 + X23 + X31 + X32 + X33 ≥ 250 Total at end of three weeks
X11 + X21 + X31 + X12 + X22 + X32 ≥ 200 Total at end of two weeks
X11 + X21 + X31 ≥ 120 Total at end of first week
X11 + X12 + X13 ≥ 0.45*250 Truck mix requirement
X21 + X22 + X23 ≥ 0.40*250 Rail mix requirement
X31 + X32 + X33 ≤ 0.15*250 Air mix limit
Xij ≥ 0 for all i and j


 
 

Final


Reduced


Objective


Allowable


Allowable
Cell Name

Value


Cost


Coefficient


Increase


Decrease
$D$6 Week 1 by Truck

45


0


200


360


1E+30
$E$6 Week 1 by Rail

60


0


140


360


1E+30
$F$6 Week 1 by Air

15


0


500


1E+30


360
$D$7 Week 2 by Truck

50


0


200


0


1E+30
$E$7 Week 2 by Rail

55


0


140


0


1E+30
$F$7 Week 2 by Air

0


360


500


1E+30


360
$D$8 Week 3 by Truck

13


0


200


1E+30


0
$E$8 Week 3 by Rail

12


0


140


60


0
$F$8 Week 3 by Air

0


360


500


1E+30


360
 
Constraints
 

Final


Shadow


Constraint


Allowable


Allowable
Cell Name

Value


Price


R.H. Side


Increase


Decrease
$D$18 Week 1 by Truck

45


−360


45


13


0
$E$18 Week 1 by Rail

60


−360


60


15


0
$F$18 Week 1 by Air

15


0


15


1E+30


0
$D$19 Week 2 by Truck

50


0


50


13


25
$E$19 Week 2 by Rail

55


0


55


12


25
$F$19 Week 2 by Air

0


0


10


1E+30


10
$D$20 Week 3 by Truck

13


0


55


1E+30


42
$E$20 Week 3 by Rail

12


0


45


1E+30


33
$F$20 Week 3 by Air

0


0


5


1E+30


5
$D$9 Shipped by Truck

108


60


108


12


13
$E$9 Shipped by Rail

127


0


100


27


1E+30
$F$13 Total Shipped Tons

250


140


250


33


0
$F$9 Shipped by Air

15


0


37.5


1E+30


22.5
$G$6 Week 1 Totals

120


360


120


0


15
$G$7 Week 2 Totals

225


0


200


25


1E+30
$G$8 Week 3 Totals

250


0


250


0


1E+30

Refer to Exhibit 4.1. Should the company negotiate for additional air delivery capacity?
No. The shadow prices for each week of air delivery are zero.

Question 45 (1 point)
 
Almost all network problems can be viewed as special cases of the
Question 45 options:


a)
transshipment problem.


b)
shortest path problem.


c)
maximal flow problem.


d)
minimal spanning tree problem.
Question 46 (1 point)
 
Decision variables in network flow problems are represented by
Question 46 options:


a)
nodes.


b)
arcs.


c)
demands.


d)
supplies.
Question 47 (1 point)
 
The arcs in a network indicate all of the following except?
Question 47 options:


a)
routes


b)
paths


c)
constraints


d)
connections
Question 48 (2 points)
 
An oil company wants to produce lube oil, gasoline and diesel fuel at two refineries at the minimum cost. There are two sources of crude oil. The following network representation depicts this problem.





Write out the LP formulation for this problem.
Minimize: 15X13 + 13X14 + 9X23 + 11X24 + 4X35 + 7X36 + 8X37 + 3X45 + 9X46 + 6X47

Subject to
-X13 - X14 = -100
-X23 - X24 = -50
0.80X13 + 0.95X23 - X35 - X36 - X37 = 0
0.85X14 + 0.85X24 - X45 - X46 - X47 = 0
0.95X35 + 0.90X45 = 50
0.90X36 + 0.95X46 = 25
0.90X37 + 0.95X47 = 75
Xij >= 0

Question 49 (2 points)
 
An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. The following Excel spreadsheet shows this problem. What formula should be entered in cell E6 (and copied to cells E7:E15) in this spreadsheet?

 
 

A


B


C


D


E


F


G


H


I


J


K


L


M

1


2


3


4


Unit


Net


Supply/

5
Flow from Node

Yield
Flow into Node

Cost


Nodes
Flow

Demand

6


1
Crude A

0.90


3
Refinery 1

15


1
Crude A

−120
7 1 Crude A 0.85 4 Refinery 2 13 2 Crude B −60

8


2
Crude B

0.80


3
Refinery 1

9


3
Refinery 1

0

9


2
Crude B

0.85


4
Refinery 2

11


4
Refinery 2

0

10


3
Refinery 1

0.95


5
Lube Oil

4


5
Lube Oil

75

11


3
Refinery 1

0.90


6
Gasoline

7


6
Gasoline

50

12


3
Refinery 1

0.90


7
Diesel

8


7
Diesel

25

13


4
Refinery 2

0.90


5
Lube Oil

3


14


4
Refinery 2

0.95


6
Gasoline

9


15


4
Refinery 2

0.95


7
Diesel

6


16


17


Total cost

D6*A6, copied to E7:E15
Question 50 (2 points)
 
An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. The following Excel spreadsheet shows this problem.

What values would you enter in the Analytic Solver Platform task pane for the following Excel spreadsheet?

Objective Cell:

Variables Cells:

Constraints Cells:

 
 

A


B


C


D


E


F


G


H


I


J


K


L


M

1


2


3


4


Unit


Net


Supply/

5


Flow from Node


Yield


Flow into Node


Cost


Nodes
Flow

Demand

6


1
Crude A

0.90


3
Refinery 1

15


1
Crude A

−120
7 1 Crude A 0.85 4 Refinery 2 13 2 Crude B −60

8


2
Crude B

0.80


3
Refinery 1

9


3
Refinery 1

0

9


2
Crude B

0.85


4
Refinery 2

11


4
Refinery 2

0

10


3
Refinery 1

0.95


5
Lube Oil

4


5
Lube Oil

75

11


3
Refinery 1

0.90


6
Gasoline

7


6
Gasoline

50

12


3
Refinery 1

0.90


7
Diesel

8


7
Diesel

25

13


4
Refinery 2

0.90


5
Lube Oil

3


14


4
Refinery 2

0.95


6
Gasoline

9


15


4
Refinery 2

0.95


7
Diesel

6


16


17


Total cost
Objective Cell: H17
Variables Cells: A6:A15
Constraints Cells:
A6:A15 ≥ 0
L6:L12 ≥ M6:M12

Question 51 (1 point)
 
A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?
Question 51 options:


a)
X1 + X2 + X3 + X4 = 1


b)
X1 + X2 + X3 + X4 ≤ 1


c)
X1 + X2 + X3 + X4 ≥ 1


d)
X1 + X2 + X3 + X4 ≥ 0
Question 52 (1 point)
 
A company wants to select no more than 2 projects from a set of 4 possible projects. Which of the following constraints ensures that no more than 2 will be selected?
Question 52 options:


a)
X1 + X2 + X3 + X4 = 2


b)
X1 + X2 + X3 + X4 ≤ 2


c)
X1 + X2 + X3 + X4 ≥ 2


d)
X1 + X2 + X3 + X4 ≥ 0
Question 53 (1 point)
 
How is an LP problem changed into an ILP problem?
Question 53 options:


a)
by adding constraints that the decision variables be non-negative.


b)
by adding integrality conditions.


c)
by adding discontinuity constraints.


d)
by making the RHS values integer.
Question 54 (1 point)
 

How is an LP problem changed into an ILP problem?

Question 54 options:


a)


by adding constraints that the decision variables be non-negative.


b)


by adding integrality conditions.


c)


by adding discontinuity constraints.


d)


by making the RHS values integer.
Question 55 (1 point)
 

The LP relaxation of an ILP problem

Question 55 options:


a)


always encompasses all the feasible integer solutions to the original ILP problem.


b)


encompasses at least 90% of the feasible integer solutions to the original ILP problem.


c)


encompasses different set of feasible integer solutions to the original ILP problem.


d)


will not contain the feasible integer solutions to the original ILP problem.
Question 56 (1 point)
 

The objective function value for the ILP problem can never

Question 56 options:


a)


be as good as the optimal solution to its LP relaxation.


b)


be as poor as the optimal solution to its LP relaxation.


c)


be worse than the optimal solution to its LP relaxation.


d)


be better than the optimal solution to its LP relaxation.