#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.

Flairís 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 arenít 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 # ___________

 

 

 

     

 

Cj

Basic

Variables

Quantity

(RHS)

 

 

 

 

 

 

 

 

 

 

 

 

 

     

 

 

           

 

 

 

 

Zj

         

Cj - Zj