EXTENDED SIMPLEX METHOD FOR CASIO CFX-9850/9860GB PLUS

About this program:  This is a front-end add-on to the program LINPROG that is archived in the Casio CFX-9850Plus calculator.  You must activate LINPROG in order to use this program.  I'll tell you how to do that  later. This add-on sets up the first feasible tableau for mixed inequalities and standard minimization problems and transfers that matrix to Mat A and calls LINPROG to provide the final solution.  This is a pseudo-menu driven program that gives solutions to standard maximization, mixed maximization, or standard minimization problems.  To solve either problem, the appropriate matrix with proper slack variables and objective function must be entered into matrix A.  Appropriate negative slack variables must entered for mixed, or minimization problems.  The objective function must be negative for maximization problems and positive for minimization problems.  Of course, you can solve standard maximization problems by entering the first tableau with appropriate positive slack variables.   

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

Memory used and entry time:  This program uses uses 383 bytes of memory and LINPROG uses 617 bytes of memory.  I estimate that it will take about 20 minutes to enter this program by hand and only about 30 seconds to load LINPROG. 

Watch Out!  You may be tempted to change some of the variables or the matrix names in this program.  Just be aware that the variables and matrix names were correlated with the program LINPROG to reduce memory usage, and to make sure that the matrix that is handed over to LINPROG is in the correct matrix position.

SNYTAX NOTE: The symbol => is not equal to or greater than, but is the symbol obtained by [SHIFT], [PRGM],[F3],[F3]. The symbol ∆ is not a triangle, but the symbol obtained by [SHIFT], [PRGM],[F3]. The symbol _| is the button ab/c.

Loading:  Okay, so how do I load LINPROG?. 
Go to the MENU, select PRGM, and press EXE.  Then press F6; then 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.  

(Notice that if you want to read any of these decimals in fractions, just scroll over the element you want to read.)
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}

_{Notice that the last row, the objective function, has negative coefficients.  Plug that into matrix A; go to your program and execute it.  At then at the prompt, press 1; then EXE. A message will appear on the screen; them after a few seconds your answer will be displayed.}

<sub>Note:  Mat F is the working matrix for maximization problems. So if you need to run the matrix again, the original is still in Mat A. Note carefully, however, that the pre-program for minimization problems stores its changes in Mat A for the LINPROG.  But I have included a line in the program to store the original matrix in Mat B.  So, you can get the original matrix back into Mat A by going to the run screen and doing the following: 
Mat B→Mat A, EXE.
Note carefully, however, that if you run a mixed or minimization problem twice in succession without performing the above operation, on the second run will store the solve matrix in Mat B, and you will have to re-enter your matrix in Mat A.

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

_{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
Notice that in this minimization problem, the objective function has positive numbers and the slack variables are negative..}

_{Enter that into matrix A; execute the program and enter 3 at the prompt, ?, and press EXE.  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

_{Using slack variables, the first tableau will be this: (Note the signs carefully.)
| 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 at the prompt, ?, and press EXE.  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: 9/30/04}