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. Report all numerical values as decimals rounded to two (2) decimal places. Show your work separately in your Excel
NOTE for parts 6, 17, 22a, 22b, 24, 25, 27, and 28: Insert the cited deliverables into spaces entered below where they are required. Failure to include these deliverables where specified will be severely penalized.
A. The Computer Services Department must decide how to allocate 21 new laptops. 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 must get at least four of the new laptops. The Production Department must get at least five of the new laptops. Because of company politics, the Finance Department must not get more than half as many of the new laptops as the Production Department. The Production Department must not get more than half of the all new laptops that are given to both the Finance and Marketing 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 copies of both the computer input and output screens.
• AND submit all of your computer files with your completed exam to the Exam 2 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. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso.
The facilities in both Manhattan and Atlanta each have the capacity to manufacture 900 units. Demand at Memphis, New Orleans, and El Paso is for 450, 500, and 620 units, respectively.
The shipping cost per component between each facility is shown in the table below. A blank cell indicates that shipping between those two facilities is not permitted.
Philadelphia Knoxville Memphis New Orleans El Paso
Manhattan $3 $2
Atlanta $2 $3
Philadelphia $2 $4 $4 $4
Knoxville $2 $2 $3 $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.
11 In 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 copies of both the computer input and output screens.
• AND submit all of your computer files with your completed exam to the Exam 2 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.
21. 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.
22. a. In new lines entered below this part, present a drawing of the initial network representation of this problem all possible the routes.
b. In new lines entered below this part, present a drawing of the initial 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.
C. The network pictured below represents the layout of computers in a wired office layout. All possible wiring paths are shown. (Some obstacles exist between computers that eliminate some possible paths.) Each node is a location of a PC and the branches represent cables connecting the computers. The number on a branch indicates the length of the path in meters. (NOTE: The figure is not drawn to scale.)
Scenario I: Suppose that Node 1 is a server that needs to be connected to each and every individual PC. The cable system used requires each PC to have a unique connection.
23. For Scenario I described above, in new lines entered below this part, state the specific type of network flow problem this is.
24. Start from Node 1. Determine, by manual calculation, the minimum total amount of cable that would be needed to connect each and every individual computer to the network server.
In lines inserted below, you MUST present HERE your full and complete step-by-step manual solution to Scenario I. Scanned images of hand-drawn figures are acceptable.
25. In new lines entered below this part, present a drawing of the final network representation for Scenario I showing only the routes that are used.
NOTE for part 25: If your network diagram is drawn in an MS Office product, copy the figure and paste it here as a picture. If your network diagram is hand drawn (neatly), scan it and paste it here as a picture.
Scenario II: Suppose now that Node 1 is the entry point for a cable system that will tie all the computers together into one network.
26. For Scenario II described the sentence above, in new lines entered below this part, state the specific type of network flow problem this is.
27. Start from Node 1. Determine, by manual calculation, the minimum total amount of cable that would be needed to link each and every individual computer into a single network.
In lines inserted below, you MUST present HERE your full and complete step-by-step manual solution to Scenario II. Scanned images of hand-drawn figures are acceptable.
28. In new lines entered below this part, present a drawing of the final network representation for Scenario II showing only the routes that are used.
NOTE for part 28: If your network diagram is drawn in an MS Office product, copy the figure and paste it here as a picture. If your network diagram is hand drawn (neatly), scan it and paste the image here as a picture.
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