EXTENDED SIMPLEX METHOD FOR TI-83Plus & TI-82

About this program:   This is a front-end add-on to the program ticsimplex_pos for users who are not familiar with using the positive slack  variables that program uses for minimization and mixed constraints.  You must have the program tisimplex_pos  entered in your calculator in order for this program to give you anything other than the initial tableau for minimizations or mixed constraints. 

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.

Note:  The answer is first displayed in decimals and paused.  If you want fractions, just press ENTER again, and fractions will be displayed when appropriate.  DO NOT look for the that displays the matrix in this program.   It's in the called program TCSMPLEX.
Now for using it:  Let's do this a maximization problem:
Maximize P = 2x₁ +4x₂ +3x_{3
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.  When the Menu appears,  enter 1. 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:
y1 + 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
400x1+160x2+280x3≤20000
x1 +x2 +x3 ≥60

Then our first tableau will be this:
_{Using slack variables, the 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 when the Menu appears.  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: 10/4/04}