College of Business

NAME ______________________________________________

College of Business

MSBA 757: PRESCRIPTIVE ANALYTICS

ME

Directions: This exam contains two (2) problems, problems A and B, each with a number of parts, for a total of 28 numbered parts for the entire test. The Midterm Exam is valued at 400 points

performed individually, alone, and on your own. Any violations will be referred to the Office of Academic Integrity for adjudication.

You may and are allowed to use your text, your notes, and any resource on the Bb course website as reference material, including my slides, my problem solutions, my worked examples, and my Excel and Lingo files. You are forbidden to use any other resources besides those just cited. Additionally, you are prohibited from discussing this exam with each other or anyone else. You are prohibited from sharing work, computer files, and drawings.

Read each part carefully and answer exactly what is asked. Insert your response to each and every part in a new line entered directly below it. Place a copy of all graphs, charts, tables, into a line directly below where it is asked to be presented. Only your Word document containing your completed exam will be graded; I will not hunt through your Excel and Lingo files searching for results, graphs, reports, etc. Report all numerical values as decimals rounded to two (2) decimal places.

Do not re-write or reformat. Do not alter the order and/or numbering of any parts. Enter your responses in Times New Roman font in black. Failure to follow any of these instructions will be severely penalized up to including not grading your exam.Enter your last name in the file name of all files submitted. The file name format is Midterm Surname.xxxx (where Surname is your last or family name and xxxx is the appropriate file extension). Type your name in the space provided at the top of this page. Type your name in the space provide below for the honor code affirmation. Type your name into an empty cell of every worksheet of your Excel file. Type your name as a comment in your Lingo files.

NOTE for parts 6, 17, 23a, and 23b: Insert the cited deliverables into spaces entered below where they are required. Failure to include these deliverables where specified will be severely penalized with a deduction of a substantial number of points.

Your completed work is to be submitted electronically to the xxxx link on the Assessments page in the Navigation bar of the course website. All of your

Moreover, submission is a one-time event. This means that there is just one.

After 11:59:00 PM, the link will close and will not be reopened, regardless of the reason or the excuse. Any files missing in your submission (e.g., any of your calculational computer files) will be assigned a grade of zero. Furthermore, e-mail submission of any of your Midterm Exam materials will not be accepted under any circumstances, regardless of the reason or the excuse. Refer to the Student Liability section of the course syllabus.Failure to follow any of the aforementioned completion and submission instructions will be severely penalized by the deduction of substantial number points from your earned score.

I affirm, under penalty of perjury, that I have complied with all the Terms and Conditions set forth for this exam. I have neither given nor received any assistance of any kind by any means on this exam. (Type your name on the line below as a proxy for your signature.)

___________________________________________________

Name

A.The Computer Services Department must decide how best to allocate all 23 new laptops it has purchased. Three different departments have been designated to receive the laptops: the Production Department, Marketing Department, and Finance Department. Each department has requested as many laptops as they can get.

The Production Department can increase its productivity by 5% for each new laptop it gets. The Marketing Department can increase its productivity by 4% for each new laptop it gets. The Finance Department can increase its productivity by 2% for each new laptop it gets.

All of the new laptops must be allocated, subject to the following constraints. The Marketing and Production Departments each must receive at least four of the new laptops. The Finance Department must get at least five of the new laptops. Furthermore, because of company politics, the Finance Department must get at least half as many of the new laptops as are allocated to the Production Department. For the same reason, the Finance Department must also get at least half as many of the new laptops as are given to the Marketing Department. The Production Department is adamant about getting at least four more of the new laptops than the Marketing Department gets. The Marketing Department must not get more than half of combined number of new laptops that are given to both the Finance and Production Departments.

The problem is to allocate all the new laptops to the Production, Finance, and Marketing Departments so as to maximize the total percent increase in productivity.

1.In new lines entered below this part, define all the decision variables. Be explicit and specific, including the units of measure.

2.In new lines entered below this part, in terms of the decision variables defined above, state mathematically the objective function.

3.In new lines entered below this part, in terms of the decision variables you defined above, state mathematically all the constraints of the situation described.

4.In new lines entered below this part, state whether or not the problem you formulated mathematically in parts 1 through 3 is a linear program (LP) or not? If it is, explain why.

5.In new lines entered below this part, if this is a linear program, then what special kind of LP problem is this and explain why.

6.Solve this problem with a computer using either Excel Solver or LINGO.

In a space created below this part, you must present HERE copies of both the computer input and output screens.

AND submit all of your computer files with your completed exam to the Midterm Exam link.

7.Based on your computer solution presented in part 6, in new lines entered below this part, state in plain language the best allocation of the new laptops and the total percent productivity increase that would result.

8.Based on your computer solution presented in part 6, in new lines entered below this part, state in plain language the precise meaning in the context of the business situation of any and all amounts of slack/surplus involved in the optimal solution.

9.Based on your computer solution presented in part 6, in new lines entered below this part, state the ranges of optimality on the productivity gain per new laptop for each department (that is, for each objective function coefficient).

10.In a new line entered below this part, state the name of the specific methodology used to solve the given problem as it is stated.

B.XYZ Clothiers designs and manufactures high-end garments for men. XYZs facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. The completed components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until they are sent on to facilities for final assembly at either Memphis, New Orleans, or El Paso.

The manufacturing facilities in Manhattan and Atlanta each manufacture 900 units. Demand in Memphis, New Orleans, and El Paso is for 450, 500, and 620 units, respectively. At present, the two warehouses each have sufficient capacity to store the combined output of both manufacturing facilities. Incomplete or partial components are rejected by quality control at both the manufacturing facilities and at the final assembly facilities.The shipping cost per component between each facility is shown in the table below.

Philadelphia Knoxville Memphis New Orleans El Paso

Manhattan $3 $2 Atlanta $2 $3 Philadelphia $2 $4 $4 $4

Knoxville $2 $3 $2 $2

The problem is to determine the best way to ship the garment components from the component manufacturing facilities to the final assembly facilities at the lowest total cost possible.

11In new lines entered below this part, define all the decision variables. Be explicit and specific (including units).

12.In new lines entered below this part, state mathematically the objective function in terms of the decision variables you defined in part 11.

13.In new lines entered below this part, state mathematically all the constraints of the situation described in terms of the decision variables you defined in part 11.

14.In new lines entered below this part, state whether or not the problem you formulated mathematically in parts 11 through 13 is a linear program (LP) or not? If it is, explain why.

15.In new lines entered below this part, state the specific special kind of LP problem it is.

16.a.In new lines entered below this part, state whether or not this problem balanced or unbalanced?

b.If it is unbalanced, in new lines entered below this part, state which way is it unbalanced and by how much.

17.Solve this problem with a computer using either Excel Solver or LINGO.

In a space created below this part, you must present HERE copies of both the computer input and output screens.

AND submit all of your computer files with your completed exam to the Midterm Exam link.

18.In new lines entered below this part, state all the routes that are used in your solution to ship the garment components from the component manufacturing facilities to the final assembly facilities.

19.In new lines entered below this part, state the amounts shipped over each route that is used to ship the garment components from the component manufacturing facilities to the final assembly facilities.

20.In new lines entered below this part, state the total cost of shipping the garment components from the component manufacturing facilities to the final assembly facilities.

21.a.In new lines entered below this part, state which facility or facilities got stuck with surplus components AND by how much.

b.In new lines entered below this part, state which facility or facilities will not have their demand met AND by how much.

22.In new lines entered below this part, state what the numerical value of each and every slack represents in the specific context of this problem.

23.a.In new lines entered below this part, present HERE a drawing of the initial network representation of this problem all possible the routes.

b.In new lines entered below this part, present HERE a drawing of the final network representation of this problem showing only the routes that are used.

On your drawing, annotate each and every route shown in your diagram with the number of components transferred and its cost.