This is a Managerial Report and must be completed following exactly the instructions and format that are given in the course syllabus.
Case: “E-Z Chairs”
E-Z Chair Corporation assembles and sells two models of recliner chairs: Regular and Deluxe. The company operates an assembly plant where it receives the parts for the chairs from contractor factories. The parts must be assembled, finished, and tested by E-Z Chairs personnel.
For the coming month, the labor hour requirements for each chair by model are:
| Activity | Regular | Deluxe |
| Assembly | 6 | 8 |
| Finishing | 9 | 12 |
| Testing | 2 | 2 |
The company has available 2,040 hours of Assembly labor, 2,520 hours of Finishing labor, and 600 hours of Testing labor. Also, the company must fulfill an existing contract for 100 Regular model chairs (it can produce more if desired but this is the minimum). Profit on the chairs is $250 per Regular model chair and $400 per Deluxe chair.
Do the following tasks:
1. Write the complete mathematical formulation to determine the optimal production solution to maximize total profit. Use as symbols X1 for the number of Regular chairs produced and X2 for the number of Deluxe chairs. If you wish, you may manually write this formulation provided your work is clear, neat, and easy to read.
2. Graphically solve this problem using 8 ½ inch by 11 inch graph paper. Label the graph axes using X1 on the X axis and X2 on the Y axis. Provide appropriate numbers on the tick marks of the axes using increments of 50 (you should number every tick mark). Be sure you show and label each constraint line. Lightly shade the feasible solution area (the feasible region). Show and label one example profit line as a dashed line using a profit of $60,000 (you may also show other profit lines if you wish). To receive credit, this graph must be accurately drawn, labeled, and easy to read.
3. Obtain the optimal solution by hand calculation. Calculate the amount of profit at the optimal solution. (Note: If visual inspection of the graph cannot adequately distinguish among multiple solution points, then manually calculate the solutions at each point and pick the one that provides the largest profit.) Circle the optimal solution point.
4. For each constraint, manually calculate the value of either the slack or surplus variable, whichever applies.
Show your work for steps 1 through 4 on separate pages and place them in your Managerial Report as numbered appendices. In the narrative of the Managerial Report, explain what you did, the meaning of your calculations, and what you conclude. Justify your conclusions.
5. Now solve this problem using QM for Windows and generate and print the following output, which you should attach to your report as numbered appendices. (NOTE: To print any report except the graph, go to File>Print and select the report. To print the graph, choose File>Print>Printgraph. Alternatively, you may use the Snipping Tool in QM to copy-and-paste the graph to a Word doc.)
a. Results (Problem/Data)
b. Ranging (QM’s name for the sensitivity report)
c. Graph
6. Check your manual results using the QM solution and correct your manual work if necessary. Then use the QM Ranging report to answer the following questions:
a. Give and explain the optimal solution obtained by QM and show how the optimal profit for the month is calculated.
b. The accountants for E-Z Chairs say they are uncertain about the estimated profit margins for each of the chair models. What is the sensitivity range (the low-to-high values) over which each profit coefficient can vary without changing the optimal solution? (This assumes only one of the two coefficients is allowed to vary.)
c. For the constraint that requires a minimum of 100 Regular model chairs, the dual value is shown as -50. If E-Z Chairs produced 101 Regular chairs next month instead of 100, what would be the change in total profit?
d. The owner of the contract offers to reduce the requirement for 100 Regular chairs to only 50 chairs in exchange for $1,000. If E-Z Chairs accepts this offer, what will be the change in total profit?
e. A competitor offers to provide E-Z Chairs 500 hours of Finishing labor next month in exchange for $20,000. Is it financially advantageous to E-Z Chairs to accept this offer? Fully explain.
