I have a quiz in Micro (below) can you assist by Saturday?
An insulation plant makes three types of insulation (types B, R and X). Each is produced on the same machine which can produce any mix of output so long as the daily total weight is no more than 70 tons. The insulation is shipped in trucks from the company loading dock which can process a maximum of 30 trucks per day. The trucks can carry any mix of types B, R and X insulation. A truckload of type B, R and X insulation weighs 1.4 tons, 2.8 tons and 1.9 tons respectively. The insulation carries a flame retarding spray that is currently in short supply and only 75 cans of the spray are available daily. A truckload of type B insulation requires 3 cans of the spray, type R requires 1 can per truckload and type X requires 2 cans per truckload. Demand for each type of insulation is very strong and the company anticipates no problem selling the plant’s entire output. The contribution margin for type B insulation is $1,425 per truckload, whereas for types R and X insulation, the contributions are $1,800 and $1237.50 per truckload, respectively. The company is interested in determining how much of each insulation type it should produce.
A. Develop the linear programming formulation for the above problem. Make sure you define and label your variables, clearly show the objective function and the relevant constraints in their algebraic form. (30 points)
B. Translate the above into a Solver formulation of the linear programming problem and solve it. Attach the spreadsheets showing the formulations, the answer report, sensitivity report and limits report. (40 points)
C. Describe the optimal production policy: (40 points)
1. How much of each insulation type (B, R and X) should be produced?
2. Identify and the slack and binding constraints at the optimal production level.
3. What is the total contribution at this production level?
D. Use the appropriate reports from the Solver output to answer the following questions. (60 points)
1. What would you be willing to pay for (i) an extra unit of machine time, (ii) an extra unit of loading dock capacity and (iii) an extra canister of flame retarding spray? Explain your reasoning.
2. Suppose the machine needs downtime for preventive maintenance that will reduce its daily total output by 10%. How will this affect your answers to Part C? Explain your reasoning.
3. Is a likely improvement in the availability of flame retarding spray (10 extra cans per day) affect your answer to Part C? Explain your reasoning.
E. The price of type X insulation has increased by $250 per truckload due to demand stemming from a new application. How will this change your answer to Part C? Explain your answer. (30 points)
Q2. (200 points)
Chuck Raverty is the managing partner of a small boutique consulting firm in which he has four senior partners available to work on four current projects for during the coming month. Chuck has assessed the fit between the skill levels of his colleagues relative to each of the four projects and has rated them on a 0-100 scale. Not surprisingly, the ratings are all fairly high, but there still are significant differences in the quality of fit. The following is a table of the ratings that he has developed:
Partner
Project
1
2
3
4
Alan
90
80
25
50
Charlie
60
70
50
65
David
70
40
80
85
Robert
65
55
60
75
Time
140
100
170
70
The last row of the table shows Chuck’s assessment of the time that it will take to complete each of the four projects.
A. Assume that each partner will be assigned only to one project. What is the assessment of partners to projects
that will maximize the sum of the assigned quality scores? Develop and write down the formal mathematical statement of the problem. (40 points).
B. Set up the Solver spreadsheet model for the problem above. Use Solver to solve the problem, obtain the relevant reports and interpret your answer. (40 points).
C. Support that each of the four partners has only 160 hours of time available in the coming month. Assume that more than one partner can work on a project. What assignment schedule will maximize the sum of the assigned quality scores? As in Part A, develop and write down the formal mathematical statement of the problem. (50 points)
D. Set up the Solver spreadsheet model for the problem in Part C. Use Solver to solve the problem in Part C, obtain the relevant reports and interpret your answer. (50 points)
E. Suppose that Chuck does not want to assign multiple partners to the same project but is willing to provide an incentive for each partner to work the overtime needed. Based on the solutions obtained in Parts B and D, develop a comparison of the quality levels of the projects that are delivered. Assuming that a point of increased project quality is worth $1,000 to him, what should he be willing to pay for the quality maximizing solution? (200 points).