#10
Mgmt 380
Assignment #4
DUE: Friday, March 3
20 points
The Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of hours of carpentry work and a certain number of labor hours in the painting and varnishing department. Each table takes 4 hours of carpentry and 2 hours in painting and varnishing. Each chair requires 3 hours in carpentry and 1 hour in painting and varnishing. During the current production period, 240 hours of carpentry time are available and 100 hours of painting and varnishing time are available. Each table yields a profit of $7; each chair produced yields $5 profit.
Flair’s wants to determine the best possible combination of tables and chairs to manufacture in order to reach the maximum profit. The firm would like this production mix situation formulated as a linear programming model and solved with both a graphical model and the simplex model.
Step 1: Define the problem.
What is the goal? What is the research question? What are the decision variables? What is the objective function? What are the constraints?
Step 2: Gather the data for the problem. (This has been provided.)
Step 3: Build one or more model(s).
In this case, you will build three:
1) mathematical (linear programming) model
2) graphical model
3) simplex model
Submit the following, stapled in order:
1) cover page with your name, course, assignment number, and signature
2) the problem definition (step 1 above)
3) the mathematical (linear programming) model
4) the graphical model:
5) the simplex model:
Keep in mind: The optimal solution acquired with the graphical method and the optimal solution acquired with the simplex method should obviously be the same. And, if Flair asked you to also do a spreadsheet model, it too would result in the same optimal solution as the graphical and simplex model. (But aren’t you glad Flair did not ask you to do this?)
Note: As with all assignments, this one must be presented in a professional manner, typed, spell-checked, and grammar-checked.
The following blank tableau is provided so that you can avoid drawing this table for each iteration. It can be copied.
Simplex Tableau for this Model
Iteration # ___________
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Basic Variables |
Quantity (RHS) |
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Cj - Zj |