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About this program:  This is not one of my programs.  It's a program that comes archived in a Casio calculator and it has to be loaded for use.   No problem, that only takes a half minute.  I'll tell you how to do it later.  This is an excellent program for doing standard maximization, mixed, and minimization problems.  It uses positive slack variables for  ≥ inequalities.  So, you must reformulate the inequalities and the objective function for some non-standard problems.  It handles standard maximization problems with no other change than entering positive slack variables.  I suggest you use this program if you know the method that uses positive slack variables for ≥, or if you have the time to learn it.  I have a program that I have written that uses negative slack variable for ≥, but it is probably not as robust as this program.  It's listed as using negative slack variables on the program list on this Website want to try to use it..   
Running the Program:
  Unlike several of my programs, the student does not participate in this program other than to enter the matrix in position A and to reformulate the matrix for the reasons I outlined above.  You must construct the first tableau and enter that in matrix A; then just execute the program and the calculator will display the answer.  The answer is not stored in a matrix.   .
Memory used and entry time:  This program uses 617 bytes of memory.  It takes only about 30 seconds to load it.  

Loading:  Okay, so how do I load it. 
Go to the MENU, select PRGM, and press EXE.  Then press F6; the F5(Load).
Scroll down to U.S.A. and highlight it; then press EXE.  That's give you a list of programs. Scroll down to LINPROG and press EXE.  That'll load the program.  

Now for using it:  Let's do this a maximization problem:
Maximize P = 2x1 +4x2 +3x3
With these constraints:
x1 +3x2 + x3 6
2x1 +2x2 +x3 5
3x1 =x2 +4x3 7

Using slack variables, the first tableau will be this:
| 1   3     1  1  0  0  6|
|2    2     1  0  1  0  5 |
|3    1    4   0  0 1  7 |
|-2  -4  -3   0  0  0 0

Plug that into matrix A; go to your program and execute it and your answer will be displayed.

Simple minimization problem: (That's about all you can do with this program.)
Minimize Q= 6y1 +4y2
With these constraints:
y1 + 3y2 ≥5
y1 + y2 ≥3
3y1 +y2 ≥5

Construct the first tableau to enter in Matrix A like this:
 Make all ≥ inequalities negative and enter positive slack variables.  Transpose the coefficient matrix; insert slack variables; use the coefficients in the Q expression as the last column; use the negative of the constants in the last row.  When you do that, you'll have this:

| -1  - 3   1  0  0  -5|
|-1    -1  0  1  0  -3 |
|-3    -1  0  0  1  -5 |
|6     4    0  0  0    0|

Enter that into matrix A; execute the program and you'll have this:
| 0    1   0  -1.5  0.5     2|
|0     0   1  -4      1       2 |
|1     0   0  0.5   -0.5     1|
|0     0   0   3      1    -14 |

So, 14 is the minimum value (the positive of the answer),  and y1=1; y2=2.

Last Revised: 8/15/03