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About this program:   This program is for those who are familiar with the simplex method that uses POSITIVE slack variables when doing problems with mixed constraints or minimization or standard maximization.  You must enter the first tableau in matrix [A] with the proper slack variables and with the proper signs for the indicator row (objective function.)  The program then manipulates rows to give a first feasible solution and displays the solution in decimal form.  The solution may be displayed in fractional form, if appropriate, by pressing ENTER.  When you are finished with the answer, press ENTER because the program is STILL RUNNING in PAUSE Mode to permit scrolling the matrix. Note that the last value in the matrix for minimization may be negative, but you can just remember that it must be positive.

Running the Program:
  Unlike several of my other programs, the student does not participate in this program other than to enter the matrix in position A and to formulate the first tableau with appropriate  slack variables.  I'll give you examples on this after the coding section. 

Memory used and entry time:  This program uses uses about 372 bits of memory.   I estimate that it will take about 15 minutes for an inexperienced programmer to enter this program by hand.

DISCLAIMER:  This program is free, and, therefore, I make no claims about it's efficacy, efficiency, or proper operation.  This is a new program as of 8/15/03.  If you find a problem with this program, or can suggest  improvements, please e-mail me at knosummath@aol.com  .

Use of this Program:   This is NOT my program and I take no credit for the program ideas or flow.  This is a translation of a program that was written by someone for a Casio Calculator.  I have not been able to determine the author.  I believe the program is the same, or almost the same, as the program called LINPROG in the Casio CFX-9850 Calculator.  I have made a few changes in the program and, of course, changed the coding symbols where appropriate, but I do not want to claim that this is my program. I have found no indication anywhere that this program is copyrighted, but to err on the side of caution, I suggest you make only one copy and be sure not to publish it for profit.  If you find that it is copyrighted, let me know and I'll immediately delete this program. 






Program designation



Lbl 0


Repeat P = 0


[B]T →[C]


For (K, 1, C-1)

If  [B](R,K) < 0    
Then: 2→P:End: End    
For (K, 1, R-1)    

If  [B](K,C) < 0

Then: 1→P: End: End    
If P=1    
Then: Matr→List([B], C, L1)    

For( K,1, R-1)


If M=L1(K)


Then: K→I:  End: End


Matr→List([C],I, L1)





If M <0    
Then: For( K,1, C-1)    

If M=L1(K)


Then: K→J: End: End


Else: 0→P:End: End

If P=2    
Then: Matr→List([C], R,L1)    
0→L1 (C): Min (L1)→M    
For (K,1,C-1)    
If M = L1(K)    
Then: K→J: End    
Matr→List([B], J,L1)    
For (K,1,R-1)    
If L1(K) > 0    
Then: L1(K)/[B](K,C)→L1(K):End    
If L1(K)< 0    
Then: 0→L1 (K): End: End    
If M > 0    
Then: For(K,1,R-1)    

If M = L1(K)

Then: K→I: End: End    
Else: 0→P: End: End    
If P≠0    
Then: *row(1/[B](I,J), [B], I)→[B]    

For (K,1, R)


If K≠I and [B](K,J)≠0

Then: *row+(-[B](K, J)), [B], I,K)→[B]    


Pause [B]    
Pause [B]►Frac    

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.     After a few seconds your answer will be displayed.

Standard Minimization problem: (Be sure you know what standard minimization means.)
Minimize w= 3y1 +2y2
With these constraints:
y 1+ 3y2 ≥6
2y1 + y2 ≥3

We can look at this problem like this:
Maximize:  z = -w= -3y1 - 2y2
Subject to:y1 + 3y2 ≥6
                   2y1 + y2 ≥3

So, our first tableau is this:
| -1  - 3    1   0  |-6
| -2   -1     0  1  |-3
|3    2     0   0  |0

Enter that into matrix A; execute the program and enter 3 when the Menu appears. The display will be  this:
|  0    1  - 0.4   0.2    1.8 |
|  1   0    0.2  -0.6     0.6 |
|  0   0    0.2   1.4     -5.4|

Notice that -5.4 is the negative of the minimum, 5.4, and that y1 = 0.6 and y2 = 1.8.

Mixed ≤ and ≥ problem:
Maximize:    Z= 120x1 + 40x2 + 60x3
Subject To: 
x1 +x2 + x3 ≤ 100
x1 +x2 +x3 ≥60

Then our first tableau will be this:
| 1      1      1    1  0  0  |100
|400 160  280  0  1  0  |20000
|-1     -1    -1     0  0 1 | -60
|-120  -40  -60   0  0  0| 0

Enter that into matrix A; execute the program and enter 2 from the Menu.  The display will be  this:
| 0      0      0    1       0           1           40
| 1      0     0.5  0   4.1E-3    0.6666     43.3333
| 0      1     0.5  0    -4E-3     -1.666      16.666
| 0      0     20   0     0.333    13.333     5866.6


Last Revised: 8/23/03
Checked:  02/13/13