Follow the following steps to walk through the solution of the online example. 1. "Open" the file Online-Example.end 2. Familiarize yourself with the layout of this window, and with how to enter problem data. (For other problems, you need to enter data yourself.) At the bottom of the window, the current settings are indicated as: Area: General Linear Programming Procedure: Enter or Revise a General Linear Programming Model Option: Tabular Form Click "Finish" at the lower-right corner when you are ready to move on. 3. Click "Procedure" at the top menu and select "Setup for the Simplex Method -- Interactive only 4. In the next window, click to select the first constraint. Then, click "OK" below to "Add Slack Variable". Repeat this for all 4 functional constraints. Click "Finish" when you are done. 5. Click "Procedure" at the top menu and select "Solve Interactively by the Simplex Method". 6. Since the current solution is not optimal, click "Next". A basic understanding of the Simplex method will be assumed from here on. (Please review online notes for details.) 7. Use the mouse to highlight the X1 column and the last row (eq. 4). Enter "2" into the blank. Click "Next". 8. In the next window, enter "-4", "2", "-3", and "0" into the blank spaces. Click "Next". 9. The result of an iteration of the Simplex method is now shown in the next window. Since the current solution is not optimal, click "Next". 10. Highlight the X2 column and Eq. 1. Enter "2" into the blank space, and click "Next". 11. In the next window, enter "-1", "3.5", "2", and "0.5" into the blank spaces. Click "Next". 12. The result of the second iteration is now shown in the next window. Since the new solution is optimal, enter "Y" into the blank and click "Next". 13. The solution is now complete. Click "File" in the top menu and select "Print to File". Supply a filename in the dialog box to save the output as a .txt file. This saved file is reproduced below. (You can paste the output as part of your howework solution.) 14. Click "Finish", and move on to another problem. ===================================================== Linear Programming Model: Number of Decision Variables: 2 Number of Functional Constraints: 4 Max Z = 4 X1 + 3 X2 subject to 1) 2 X1 + 3 X2 <= 6 2) -3 X1 + 2 X2 <= 3 3) 0 X1 + 2 X2 <= 5 4) 2 X1 + 1 X2 <= 4 and X1 >= 0, X2 >= 0. Solve Interactively by the Simplex Method: Bas|Eq| Coefficient of | Right Var|No| Z| X1 X2 X3 X4 X5 X6 | side ___|__|__|_____________________________________|______ | | | | Z | 0| 1| -4 -3 0 0 0 0 | 0 X3| 1| 0| 2 3 1 0 0 0 | 6 X4| 2| 0| -3 2 0 1 0 0 | 3 X5| 3| 0| 0 2 0 0 1 0 | 5 X6| 4| 0| 2* 1 0 0 0 1 | 4 Bas|Eq| Coefficient of | Right Var|No| Z| X1 X2 X3 X4 X5 X6 | side ___|__|__|_____________________________________|______ | | | | Z | 0| 1| 0 -1 0 0 0 2 | 8 X3| 1| 0| 0 2* 1 0 0 -1 | 2 X4| 2| 0| 0 3.5 0 1 0 1.5 | 9 X5| 3| 0| 0 2 0 0 1 0 | 5 X1| 4| 0| 1 0.5 0 0 0 0.5 | 2 Bas|Eq| Coefficient of | Right Var|No| Z| X1 X2 X3 X4 X5 X6 | side ___|__|__|_____________________________________|______ | | | | Z | 0| 1| 0 0 0.5 0 0 1.5 | 9 X2| 1| 0| 0 1 0.5 0 0 -0.5 | 1 X4| 2| 0| 0 0 -1.75 1 0 3.25 | 5.5 X5| 3| 0| 0 0 -1 0 1 1 | 3 X1| 4| 0| 1 0 -0.25 0 0 0.75 | 1.5 ===========================================================