26 October 2023   8:33:23.236 AM
MATMAN, version 1.61
Last modified on 01 July 2000.
 
An interactive program to perform elementary
row and column operations on a matrix, or
the simplex method of linear programming.
 
Developed by Charles Cullen and John Burkardt.
All rights reserved by the authors.  This program may
not be reproduced in any form without written permission.
 
Send comments to burkardt@psc.edu.
 
Enter command? ("H" for help)
Enter file name, default= "matman.lpt".
Opening the transcript file "output.txt".
 
Enter command? ("H" for help)
Paging turned OFF.
 
Enter command? ("H" for help)
A(I,J)=S  Set matrix entry to S.
CHECK checks if the matrix is row reduced.
E     enters a matrix to work on.
HELP  for full help.
L     switches to linear programming.
Q     quits.
Z     automatic row reduction (requires password).
?     for interactive help.
 
R1 <=> R2  interchanges two rows
R1 <= S R1 multiplies a row by S.
R1 <= R1 + S R2 adds a multiple of another row.
 
 
Enter command? ("H" for help)
 
Here is a list of all MATMAN commands:
 
A(I,J)=S  Set matrix entry to S.
B      Set up sample problem.
BASIC I, J changes basic variable I to J.
CHECK  Check matrix for reduced row echelon form.
CHECK  Check linear program table for optimality.
COL_AUTO  Automatic column reduction.
DEC    Use decimal arithmetic.
DEC_DIGIT Set the number of decimal digits.
E      Enter matrix with I rows and J columns.
E      Enter a linear program, I constraints, J variables.
G      Add/delete a row or column of the matrix.
H      for quick help.
HELP   for full help (this list).
I_BIG  Set size of largest integer for fractions.
INIT   Initialize data.
J      Jacobi rotation in (I,J) plane.
K      Open/close the transcript file.
L      To switch between linear algebra and linear programming.
P      Pivot linear program, entering I, departing J.
Q      Quit.
RES    Restore a saved matrix or table
RAT    Use rational arithmetic.
REAL   Use real arithmetic.
ROW_AUTO  Automatic row reduction.
S      Store the current matrix or table.
T      Type out the matrix
TS     Type linear programming solution.
U      Undo last operation.
V      Remove LP artificial variables.
W/X    Write/read example to/from file.
Y      Turn automatic printing ON or OFF.
#      Begins a comment line.
<      Get input from a file.
%/$    Turn paging on/off.
 
R1 <=> R2  interchanges two rows.
R1 <= S R1 multiplies a row by S.
R1 <= R1 + S R2 adds a multiple of another row.
 
C1 <=> C2  interchanges two columns.
C1 <= S C1 multiplies a column by S.
C1 <= C1 + S C2 adds a multiple of another column.
 
Enter command? ("H" for help)
You are already using the arithmetic type that
you have requested.
 
Enter command? ("H" for help)
Enter number of rows, number of columns.
Enter entries 1 to 3 of row 1
Enter entries 1 to 3 of row 2
Enter entries 1 to 3 of row 3
A copy of this matrix is being saved.
 
  The current matrix:
 
    1    2    3
 
    4    5    6
 
    7    8   11
 
Enter command? ("H" for help)
  ERO: Row 1 <=> Row 3
 
  The current matrix:
 
    7    8   11
 
    4    5    6
 
    1    2    3
 
Enter command? ("H" for help)
  ERO: Row 1 <=  Row 1 / 7
 
  The current matrix:
 
    1    8   11
         7    7
 
    4    5    6
 
    1    2    3
 
Enter command? ("H" for help)
  ERO: Row 2 <=  Row 2 - 4 Row 1
 
  The current matrix:
 
    1    8   11
         7    7
 
    0    3   -2
         7    7
 
    1    2    3
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 - Row 1
 
  The current matrix:
 
    1    8   11
         7    7
 
    0    3   -2
         7    7
 
    0    6   10
         7    7
 
Enter command? ("H" for help)
  ERO: Row 2 <=> Row 3
 
  The current matrix:
 
    1    8   11
         7    7
 
    0    6   10
         7    7
 
    0    3   -2
         7    7
 
Enter command? ("H" for help)
  ERO: Row 2 <=  Row 2 * 7/6
 
  The current matrix:
 
    1    8   11
         7    7
 
    0    1    5
              3
 
    0    3   -2
         7    7
 
Enter command? ("H" for help)
  ERO: Row 1 <=  Row 1 - 8/7 Row 2
 
  The current matrix:
 
   1   0  -1
           3
 
   0   1   5
           3
 
   0   3  -2
       7   7
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 - 3/7 Row 2
 
  The current matrix:
 
   1   0  -1
           3
 
   0   1   5
           3
 
   0   0  -1
 
Enter command? ("H" for help)
You must use REAL arithmetic!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
  ERO: Row 3 <= - Row 3
 
  The current matrix:
 
   1   0  -1
           3
 
   0   1   5
           3
 
   0   0   1
 
Enter command? ("H" for help)
  ERO: Row 1 <=  Row 1 + 1/3 Row 3
 
  The current matrix:
 
   1   0   0
 
   0   1   5
           3
 
   0   0   1
 
Enter command? ("H" for help)
  ERO: Row 2 <=  Row 2 - 5/3 Row 3
 
  The current matrix:
 
   1   0   0
 
   0   1   0
 
   0   0   1
 
Enter command? ("H" for help)
Enter number of rows, number of columns.
Enter entries 1 to 3 of row 1
Enter entries 1 to 3 of row 2
Enter entries 1 to 3 of row 3
A copy of this matrix is being saved.
 
  The current matrix:
 
   1   2   3
 
   4   5   6
 
   7   8   9
 
Enter command? ("H" for help)
 
  ERO: Row 3 <=> Row 1
  ERO: Row 1 <=  Row 1 / 7
  ERO: Row 2 <=  Row 2 - 4 Row 1
  ERO: Row 3 <=  Row 3 - Row 1
 
  ERO: Row 3 <=> Row 2
  ERO: Row 2 <=  Row 2 * 7/6
  ERO: Row 1 <=  Row 1 - 8/7 Row 2
  ERO: Row 3 <=  Row 3 - 3/7 Row 2
 
  The current matrix:
 
   1   0  -1
 
   0   1   2
 
   0   0   0
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "31984"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
Enter entries 1 to 3 of row 3
 
  The current matrix:
 
    1    0   -1
 
    0    1    2
 
   61   31   63
   10    5   10
 
    0    0    0
 
Enter command? ("H" for help)
Your ECO command could not be understood.
The assignment symbol <=> was missing.
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
The column has been deleted!
 
  The current matrix:
 
    1   -1
 
    0    2
 
   61   63
   10   10
 
    0    0
 
Enter command? ("H" for help)
 
The following examples are available:
  "E" for eigenvalues;
  "I" for inverse;
  "S" for linear solve.
 
  "C" to cancel.
 
No problem was selected.
 
  The current matrix:
 
   0   0
 
   0   0
 
   0   0
 
   0   0
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "4"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "det"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
  The current matrix:
 
  0.  0.
  0.  0.
  0.  0.
  0.  0.
 
Enter command? ("H" for help)
Enter number of rows, number of columns.
Enter entries 1 to 3 of row 1
Enter entries 1 to 3 of row 2
Enter entries 1 to 3 of row 3
A copy of this matrix is being saved.
 
  The current matrix:
 
    1.    2.    3.
    4.    5.    6.
    7.    8.   11.
 
Enter command? ("H" for help)
  ERO: Row 1 <=> Row 3
 
  The current matrix:
 
    7.    8.   11.
    4.    5.    6.
    1.    2.    3.
 
Enter command? ("H" for help)
  ERO: Row 1 <=  Row 1 / 7
 
  The current matrix:
 
   1.0000000   1.1428571   1.5714286
   4.0000000   5.0000000   6.0000000
   1.0000000   2.0000000   3.0000000
 
Enter command? ("H" for help)
  ERO: Row 2 <=  Row 2 - 4 Row 1
 
  The current matrix:
 
   1.0000000   1.1428571   1.5714286
   0.0000000   0.4285714  -0.2857143
   1.0000000   2.0000000   3.0000000
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 - Row 1
 
  The current matrix:
 
   1.0000000   1.1428571   1.5714286
   0.0000000   0.4285714  -0.2857143
   0.0000000   0.8571429   1.4285714
 
Enter command? ("H" for help)
 
Enter command? ("H" for help)
  ERO: Row 2 <=> Row 3
 
  The current matrix:
 
   1.0000000   1.1428571   1.5714286
   0.0000000   0.8571429   1.4285714
   0.0000000   0.4285714  -0.2857143
 
Enter command? ("H" for help)
  ERO: Row 2 <=  Row 2 / 0.857143
 
  The current matrix:
 
   1.0000000   1.1428571   1.5714286
   0.0000000   1.0000001   1.6666668
   0.0000000   0.4285714  -0.2857143
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 - 0.428571 Row 2
 
  The current matrix:
 
   1.0000000   1.1428571   1.5714286
   0.0000000   1.0000001   1.6666668
   0.0000000   0.0000002  -0.9999997
 
Enter command? ("H" for help)
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 / -1.00000
 
  The current matrix:
 
   1.0000000   1.1428571   1.5714286
   0.0000000   1.0000001   1.6666668
  -0.0000000  -0.0000002   1.0000001
 
Enter command? ("H" for help)
Enter row I, column J.
 
I_READ - Fatal error!
  S_TO_I returned error flag!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
Your ECO command could not be understood.
The assignment symbol <=> was missing.
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
Enter row I, column J.
 
I_READ - Fatal error!
  S_TO_I returned error flag!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
Enter number of rows, number of columns.
Enter entries 1 to 3 of row 1
Enter entries 1 to 3 of row 2
Enter entries 1 to 3 of row 3
A copy of this matrix is being saved.
 
  The current matrix:
 
   1.   2.   3.
   4.   5.   6.
   7.   8.   9.
 
Enter command? ("H" for help)
 
  ERO: Row 3 <=> Row 1
  ERO: Row 1 <=  Row 1 / 7
  ERO: Row 2 <=  Row 2 - 4 Row 1
  ERO: Row 3 <=  Row 3 - Row 1
 
  ERO: Row 3 <=> Row 2
  ERO: Row 2 <=  Row 2 / 0.857143
  ERO: Row 1 <=  Row 1 - 1.14286 Row 2
  ERO: Row 3 <=  Row 3 - 0.428571 Row 2
 
  ERO: Row 3 <=  Row 3 / -0.777156E-15
  ERO: Row 1 <=  Row 1 + 1.00000 Row 3
  ERO: Row 2 <=  Row 2 - 2.00000 Row 3
 
  The current matrix:
 
   1.   0.   0.
   0.   1.   0.
  -0.  -0.   1.
 
Enter command? ("H" for help)
Enter entries 1 to 3 of row 3
 
  The current matrix:
 
   1.0000000   0.0000000   0.0000000
   0.0000000   1.0000000   0.0000000
   6.1000000   6.2000000   6.3000000
  -0.0000000  -0.0000000   1.0000000
 
Enter command? ("H" for help)
Your ECO command could not be understood.
The assignment symbol <=> was missing.
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
The column has been deleted!
 
  The current matrix:
 
   1.0000000   0.0000000
   0.0000000   0.0000000
   6.1000000   6.3000000
  -0.0000000   1.0000000
 
Enter command? ("H" for help)
 
The following examples are available:
  "E" for eigenvalues;
  "I" for inverse;
  "S" for linear solve.
 
  "C" to cancel.
 
No problem was selected.
 
  The current matrix:
 
  0.  0.
  0.  0.
  0.  0.
  0.  0.
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "4"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "det"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "n"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
  The current matrix:
 
       0   0
       0   0
       0   0
       0   0
 
Enter command? ("H" for help)
Enter number of rows, number of columns.
Enter entries 1 to 3 of row 1
Enter entries 1 to 3 of row 2
Enter entries 1 to 3 of row 3
A copy of this matrix is being saved.
 
  The current matrix:
 
        1    2    3
        4    5    6
        7    8   11
 
Enter command? ("H" for help)
  ERO: Row 1 <=> Row 3
 
  The current matrix:
 
        7    8   11
        4    5    6
        1    2    3
 
Enter command? ("H" for help)
  ERO: Row 1 <=  Row 1 / 7
 
  The current matrix:
 
           1   1.143   1.571
           4       5       6
           1       2       3
 
Enter command? ("H" for help)
  ERO: Row 2 <=  Row 2 - 4 Row 1
 
  The current matrix:
 
            1    1.143    1.571
            0    0.428   -0.284
            1        2        3
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 - Row 1
 
  The current matrix:
 
            1    1.143    1.571
            0    0.428   -0.284
            0    0.857    1.429
 
Enter command? ("H" for help)
 
Enter command? ("H" for help)
  ERO: Row 2 <=> Row 3
 
  The current matrix:
 
            1    1.143    1.571
            0    0.857    1.429
            0    0.428   -0.284
 
Enter command? ("H" for help)
  ERO: Row 2 <=  Row 2 / 0.8571
 
  The current matrix:
 
            1    1.143    1.571
            0   0.9999    1.667
            0    0.428   -0.284
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 - 0.4284 Row 2
 
  The current matrix:
 
             1     1.143     1.571
             0    0.9999     1.667
             0   -0.0003   -0.9981
 
Enter command? ("H" for help)
 
Enter command? ("H" for help)
  ERO: Row 3 <=  Row 3 / -0.9996
 
  The current matrix:
 
               1       1.143       1.571
               0      0.9999       1.667
               0   0.0003001      0.9985
 
Enter command? ("H" for help)
 
Enter command? ("H" for help)
You must use REAL arithmetic!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
Enter number of rows, number of columns.
Enter entries 1 to 3 of row 1
Enter entries 1 to 3 of row 2
Enter entries 1 to 3 of row 3
A copy of this matrix is being saved.
 
  The current matrix:
 
       1   2   3
       4   5   6
       7   8   9
 
Enter command? ("H" for help)
 
  ERO: Row 3 <=> Row 1
  ERO: Row 1 <=  Row 1 / 7
  ERO: Row 2 <=  Row 2 - 4 Row 1
  ERO: Row 3 <=  Row 3 - Row 1
 
  ERO: Row 3 <=> Row 2
  ERO: Row 2 <=  Row 2 / 0.857
  ERO: Row 1 <=  Row 1 - 1.143 Row 2
  ERO: Row 3 <=  Row 3 - 0.428 Row 2
 
  The current matrix:
 
        1    0   -1
        0    1    2
        0    0    0
 
Enter command? ("H" for help)
Enter entries 1 to 3 of row 3
 
  The current matrix:
 
         1     0    -1
         0     1     2
       6.1   6.2   6.3
         0     0     0
 
Enter command? ("H" for help)
Your ECO command could not be understood.
The assignment symbol <=> was missing.
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
The column has been deleted!
 
  The current matrix:
 
         1    -1
         0     2
       6.1   6.3
         0     0
 
Enter command? ("H" for help)
 
The following examples are available:
  "E" for eigenvalues;
  "I" for inverse;
  "S" for linear solve.
 
  "C" to cancel.
 
No problem was selected.
 
  The current matrix:
 
       0   0
       0   0
       0   0
       0   0
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "4"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
MATMAN did not recogize your command:
  "det"
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
  The current matrix:
 
  0.  0.
  0.  0.
  0.  0.
  0.  0.
 
Enter command? ("H" for help)
 
The following examples are available:
  "E" for eigenvalues;
  "I" for inverse;
  "S" for linear solve.
 
  "C" to cancel.
 
Enter number of rows desired.
 
I_READ - Fatal error!
  S_TO_I returned error flag!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
The value of I, the row index, is illegal.
 
The value of I, the row index, is illegal.
 
Enter row I, column J, or "Q" to quit.
 
I_READ - Fatal error!
  S_TO_I returned error flag!
 
Enter command? ("H" for help)
Switching to linear programming mode.
Enter "Y" to use current matrix in linear programming.
 
Enter command? ("H" for help)
 
Enter command? ("H" for help)
 
The following examples are available:
  "S" a simple linear programming problem;
  "A" an advanced linear programming problem.
 
  "C" to cancel.
 
 
Simple linear programming problem:
 
Maximize:
  Z = 120 X + 100 Y + 70
subject to
  2 X + 2 Y < 8
  5 X + 3 Y < 15
 
 
  The linear programming table:
 
         1     2     3     4     P     C
 
X3       2     2     1     0     0     8
 
X4       5     3     0     1     0    15
 
Obj   -120  -100     0     0     1    70
 
Enter command? ("H" for help)
 
A(I,J)=S  Set table entry to S.
CHECK checks if the solution is optimal.
E     Enters a table to work on.
HELP  for full help.
L     switches to linear algebra.
P     I, J performs a pivot operation.
Q     quits.
TS    types the linear programming solution.
V     removes artificial variables.
Z     automatic solution (requires password).
?     interactive help.
 
R1 <=> R2  interchanges two rows
R1 <= S R1 multiplies a row by S.
R1 <= R1 + S R2 adds a multiple of another row.
 
 
Enter command? ("H" for help)
 
Objective row
 
         1     2     3     4     P     C
 
Obj   -120  -100     0     0     1    70
 
Variable with most negative objective coefficient?
 
The entering variable is 1
 
Variable with smallest nonnegative feasibility ratio?
 
Nonnegative feasibility ratios:
 
Row 1, variable 3, ratio = 4.00000
Row 2, variable 4, ratio = 3.00000
 
 
The departing variable is 4 with feasibility ratio 3
 
  ERO: Row 2 <=  Row 2 / 5
  ERO: Row 1 <=  Row 1 - 2 Row 2
  ERO: Row 3 <=  Row 3 + 120 Row 2
 
The objective changed from 70
to 430
 
  The linear programming table:
 
         1     2     3     4     P     C
 
X3       0     4     1    -2     0     2
               5           5
 
X1       1     3     0     1     0     3
               5           5
 
Obj      0   -28     0    24     1   430
 
Enter command? ("H" for help)
 
Objective row
 
         1     2     3     4     P     C
 
Obj      0   -28     0    24     1   430
 
Variable with most negative objective coefficient?
 
The entering variable is 2
 
Variable with smallest nonnegative feasibility ratio?
 
Nonnegative feasibility ratios:
 
Row 1, variable 3, ratio = 2.50000 = 5/2
Row 2, variable 1, ratio = 5.00000
 
 
The departing variable is 3 with feasibility ratio 2.50000
 
  ERO: Row 1 <=  Row 1 * 5/4
  ERO: Row 2 <=  Row 2 - 3/5 Row 1
  ERO: Row 3 <=  Row 3 + 28 Row 1
 
The objective changed from 430
to 500
 
  The linear programming table:
 
         1     2     3     4     P     C
 
X2       0     1     5    -1     0     5
                     4     2           2
 
X1       1     0    -3     1     0     3
                     4     2           2
 
Obj      0     0    35    10     1   500
 
Enter command? ("H" for help)
You must use REAL arithmetic!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
  The linear programming table:
 
                 1             2             3             4             P
 
X2       0.0000000     1.0000000     1.2500000    -0.5000000     0.0000000
X1       1.0000000     0.0000000    -0.7500000     0.5000000     0.0000000
Obj      0.0000000     0.0000000    35.0000000    10.0000000     1.0000000
 
                 C
 
X2       2.5000000
X1       1.5000000
Obj    500.0000000
 
Enter command? ("H" for help)
 
The following examples are available:
  "S" a simple linear programming problem;
  "A" an advanced linear programming problem.
 
  "C" to cancel.
 
 
Simple linear programming problem:
 
Maximize:
  Z = 120 X + 100 Y + 70
subject to
  2 X + 2 Y < 8
  5 X + 3 Y < 15
 
 
  The linear programming table:
 
          1      2      3      4      P      C
 
X3       2.     2.     1.     0.     0.     8.
X4       5.     3.     0.     1.     0.    15.
Obj   -120.  -100.     0.     0.     1.    70.
 
Enter command? ("H" for help)
 
Objective row
 
          1      2      3      4      P      C
 
Obj   -120.  -100.     0.     0.     1.    70.
 
Variable with most negative objective coefficient?
 
The entering variable is 1
 
Variable with smallest nonnegative feasibility ratio?
 
Nonnegative feasibility ratios:
 
Row 1, variable 3, ratio = 4.00000
Row 2, variable 4, ratio = 3.00000
 
 
The departing variable is 4 with feasibility ratio 3
 
  ERO: Row 2 <=  Row 2 / 5
  ERO: Row 1 <=  Row 1 - 2 Row 2
  ERO: Row 3 <=  Row 3 + 120 Row 2
 
The objective changed from 70 to 430
 
  The linear programming table:
 
                 1             2             3             4             P
 
X3       0.0000000     0.8000000     1.0000000    -0.4000000     0.0000000
X1       1.0000000     0.6000000     0.0000000     0.2000000     0.0000000
Obj      0.0000000   -28.0000000     0.0000000    24.0000000     1.0000000
 
                 C
 
X3       2.0000000
X1       3.0000000
Obj    430.0000000
 
Enter command? ("H" for help)
 
Objective row
 
          1      2      3      4      P      C
 
Obj      0.   -28.     0.    24.     1.   430.
 
Variable with most negative objective coefficient?
 
The entering variable is 2
 
Variable with smallest nonnegative feasibility ratio?
 
Nonnegative feasibility ratios:
 
Row 1, variable 3, ratio = 2.50000
Row 2, variable 1, ratio = 5.00000
 
 
The departing variable is 3 with feasibility ratio 2.50000
 
  ERO: Row 1 <=  Row 1 / 0.800000
  ERO: Row 2 <=  Row 2 - 0.600000 Row 1
  ERO: Row 3 <=  Row 3 + 28 Row 1
 
The objective changed from 430 to 500
 
  The linear programming table:
 
                 1             2             3             4             P
 
X2       0.0000000     1.0000000     1.2500000    -0.5000000     0.0000000
X1       1.0000000     0.0000000    -0.7500000     0.5000000     0.0000000
Obj      0.0000000     0.0000000    35.0000000    10.0000000     1.0000000
 
                 C
 
X2       2.5000000
X1       1.5000000
Obj    500.0000000
 
Enter command? ("H" for help)
You cannot be in linear programming mode!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
  The linear programming table:
 
           1       2       3       4       P       C
 
X2         0       1    1.25    -0.5       0     2.5
X1         1       0   -0.75     0.5       0     1.5
Obj        0       0      35      10       1     500
 
Enter command? ("H" for help)
 
The following examples are available:
  "S" a simple linear programming problem;
  "A" an advanced linear programming problem.
 
  "C" to cancel.
 
 
Simple linear programming problem:
 
Maximize:
  Z = 120 X + 100 Y + 70
subject to
  2 X + 2 Y < 8
  5 X + 3 Y < 15
 
 
  The linear programming table:
 
          1      2      3      4      P      C
 
X3        2      2      1      0      0      8
X4        5      3      0      1      0     15
Obj    -120   -100      0      0      1     70
 
Enter command? ("H" for help)
 
Objective row
 
          1      2      3      4      P      C
 
Obj    -120   -100      0      0      1     70
 
Variable with most negative objective coefficient?
 
The entering variable is 1
 
Variable with smallest nonnegative feasibility ratio?
 
Nonnegative feasibility ratios:
 
Row 1, variable 3, ratio = 4.00000
Row 2, variable 4, ratio = 3.00000
 
 
The departing variable is 4 with feasibility ratio 3
 
  ERO: Row 2 <=  Row 2 / 5
  ERO: Row 1 <=  Row 1 - 2 Row 2
  ERO: Row 3 <=  Row 3 + 120 Row 2
 
The objective changed from 70 to 430
 
  The linear programming table:
 
          1      2      3      4      P      C
 
X3        0    0.8      1   -0.4      0      2
X1        1    0.6      0    0.2      0      3
Obj       0    -28      0     24      1    430
 
Enter command? ("H" for help)
 
Objective row
 
         1     2     3     4     P     C
 
Obj      0   -28     0    24     1   430
 
Variable with most negative objective coefficient?
 
The entering variable is 2
 
Variable with smallest nonnegative feasibility ratio?
 
Nonnegative feasibility ratios:
 
Row 1, variable 3, ratio = 2.50000
Row 2, variable 1, ratio = 5.00000
 
 
The departing variable is 3 with feasibility ratio 2.50000
 
  ERO: Row 1 <=  Row 1 / 0.8
  ERO: Row 2 <=  Row 2 - 0.6 Row 1
  ERO: Row 3 <=  Row 3 + 28 Row 1
 
The objective changed from 430 to 500
 
  The linear programming table:
 
           1       2       3       4       P       C
 
X2         0       1    1.25    -0.5       0     2.5
X1         1       0   -0.75     0.5       0     1.5
Obj        0       0      35      10       1     500
 
Enter command? ("H" for help)
You must use REAL arithmetic!
 
MATMAN could not carry out your command:
 
Enter command? ("H" for help)
 
  The linear programming table:
 
         1     2     3     4     P     C
 
X2       0     1     5    -1     0     5
                     4     2           2
 
X1       1     0    -3     1     0     3
                     4     2           2
 
Obj      0     0    35    10     1   500
 
Enter command? ("H" for help)
 
The following examples are available:
  "S" a simple linear programming problem;
  "A" an advanced linear programming problem.
 
  "C" to cancel.
 
 
Advanced linear programming problem:
 
Maximize
  Z=40 X + 30 Y
subject to
  X + 2 Y > 6
2 X +   Y > 4
  X +   Y < 5
2 X +   Y < 8
 
 
  The linear programming table:
 
        1    2    3    4    5    6    7    8    P    C
 
X7      1    2   -1    0    0    0    1    0    0    6
 
X8      2    1    0   -1    0    0    0    1    0    4
 
X5      1    1    0    0    1    0    0    0    0    5
 
X6      2    1    0    0    0    1    0    0    0    8
 
Obj2    0    0    0    0    0    0    1    1    1    0
 
Obj   -40  -30    0    0    0    0    0    0    1    0
 
Enter command? ("H" for help)
 
The objective entry in column 7 is not zero,
but this corresponds to a basic variable.
 
  ERO: Row 5 <=  Row 5 - Row 1
 
The objective entry in column 8 is not zero,
but this corresponds to a basic variable.
 
  ERO: Row 5 <=  Row 5 - Row 2
 
The entering variable is 2
 
The departing variable is 7 with feasibility ratio 3
 
  ERO: Row 1 <=  Row 1 / 2
  ERO: Row 2 <=  Row 2 - Row 1
  ERO: Row 3 <=  Row 3 - Row 1
  ERO: Row 4 <=  Row 4 - Row 1
  ERO: Row 5 <=  Row 5 + 3 Row 1
 
The objective changed from -10
to -1
 
The entering variable is 1
 
The departing variable is 8 with feasibility ratio 0.666667
 
  ERO: Row 2 <=  Row 2 * 2/3
  ERO: Row 1 <=  Row 1 - 1/2 Row 2
  ERO: Row 3 <=  Row 3 - 1/2 Row 2
  ERO: Row 4 <=  Row 4 - 3/2 Row 2
  ERO: Row 5 <=  Row 5 + 3/2 Row 2
 
The objective changed from -1
to 0
 
Optimality test
 
 
Are all objective entries nonnegative?
 
Yes.  The current solution is optimal.
 
The linear programming solution:
 
       1   2   3   4   5   6   7   8
 
       2   8   0   0   5   4   0   0
       3   3           3
 
Objective = 0
 
This problem has artificial variables.
Use the "V" command to remove them.
 
  The linear programming table:
 
        1    2    3    4    5    6    7    8    P    C
 
X2      0    1   -2    1    0    0    2   -1    0    8
                  3    3              3    3         3
 
X1      1    0    1   -2    0    0   -1    2    0    2
                  3    3              3    3         3
 
X5      0    0    1    1    1    0   -1   -1    0    5
                  3    3              3    3         3
 
X6      0    0    0    1    0    1    0   -1    0    4
 
Obj2    0    0    0    0    0    0    1    1    1    0
 
Obj   -40  -30    0    0    0    0    0    0    1    0
 
Enter command? ("H" for help)
 
All the artificial variables were deleted.
The original objective function is restored.
 
You must now use the "A" command to zero out
objective row entries for all basic variables.
 
  The linear programming table:
 
        1    2    3    4    5    6    P    C
 
X2      0    1   -2    1    0    0    0    8
                  3    3                   3
 
X1      1    0    1   -2    0    0    0    2
                  3    3                   3
 
X5      0    0    1    1    1    0    0    5
                  3    3                   3
 
X6      0    0    0    1    0    1    0    4
 
Obj   -40  -30    0    0    0    0    1    0
 
Enter command? ("H" for help)
  ERO: Row 5 <=  Row 5 + 40 Row 2
 
  The linear programming table:
 
        1    2    3    4    5    6    P    C
 
X2      0    1   -2    1    0    0    0    8
                  3    3                   3
 
X1      1    0    1   -2    0    0    0    2
                  3    3                   3
 
X5      0    0    1    1    1    0    0    5
                  3    3                   3
 
X6      0    0    0    1    0    1    0    4
 
Obj     0  -30   40  -80    0    0    1   80
                  3    3                   3
 
Enter command? ("H" for help)
  ERO: Row 5 <=  Row 5 + 30 Row 1
 
  The linear programming table:
 
         1     2     3     4     5     6     P     C
 
X2       0     1    -2     1     0     0     0     8
                     3     3                       3
 
X1       1     0     1    -2     0     0     0     2
                     3     3                       3
 
X5       0     0     1     1     1     0     0     5
                     3     3                       3
 
X6       0     0     0     1     0     1     0     4
 
Obj      0     0   -20   -50     0     0     1   320
                     3     3                       3
 
Enter command? ("H" for help)
 
The entering variable is 4
 
The departing variable is 6 with feasibility ratio 4
 
  ERO: Row 1 <=  Row 1 - 1/3 Row 4
  ERO: Row 2 <=  Row 2 + 2/3 Row 4
  ERO: Row 3 <=  Row 3 - 1/3 Row 4
  ERO: Row 5 <=  Row 5 + 50/3 Row 4
 
The objective changed from 320/3 = 106.667
to 520/3 = 173.333
 
The entering variable is 3
 
The departing variable is 5 with feasibility ratio 1
 
  ERO: Row 3 <=  Row 3 * 3
  ERO: Row 1 <=  Row 1 + 2/3 Row 3
  ERO: Row 2 <=  Row 2 - 1/3 Row 3
  ERO: Row 5 <=  Row 5 + 20/3 Row 3
 
The objective changed from 520/3 = 173.333
to 180
 
Optimality test
 
 
Are all objective entries nonnegative?
 
Yes.  The current solution is optimal.
 
The linear programming solution:
 
       1   2   3   4   5   6
 
       3   2   1   4   0   0
 
Objective = 180
 
  The linear programming table:
 
         1     2     3     4     5     6     P     C
 
X2       0     1     0     0     2    -1     0     2
 
X1       1     0     0     0    -1     1     0     3
 
X3       0     0     1     0     3    -1     0     1
 
X4       0     0     0     1     0     1     0     4
 
Obj      0     0     0     0    20    10     1   180
 
Enter command? ("H" for help)
 
  The linear programming table:
 
          1      2      3      4      5      6      P      C
 
X2       0.     1.     0.     0.     2.    -1.     0.     2.
X1       1.     0.     0.     0.    -1.     1.     0.     3.
X3       0.     0.     1.     0.     3.    -1.     0.     1.
X4       0.     0.     0.     1.     0.     1.     0.     4.
Obj      0.     0.     0.     0.    20.    10.     1.   180.
 
Enter command? ("H" for help)
 
The following examples are available:
  "S" a simple linear programming problem;
  "A" an advanced linear programming problem.
 
  "C" to cancel.
 
 
Advanced linear programming problem:
 
Maximize
  Z=40 X + 30 Y
subject to
  X + 2 Y > 6
2 X +   Y > 4
  X +   Y < 5
2 X +   Y < 8
 
 
  The linear programming table:
 
         1     2     3     4     5     6     7     8     P     C
 
X7      1.    2.   -1.    0.    0.    0.    1.    0.    0.    6.
X8      2.    1.    0.   -1.    0.    0.    0.    1.    0.    4.
X5      1.    1.    0.    0.    1.    0.    0.    0.    0.    5.
X6      2.    1.    0.    0.    0.    1.    0.    0.    0.    8.
Obj2    0.    0.    0.    0.    0.    0.    1.    1.    1.    0.
Obj   -40.  -30.    0.    0.    0.    0.    0.    0.    1.    0.
 
Enter command? ("H" for help)
 
The objective entry in column 7 is not zero,
but this corresponds to a basic variable.
 
  ERO: Row 5 <=  Row 5 - Row 1
 
The objective entry in column 8 is not zero,
but this corresponds to a basic variable.
 
  ERO: Row 5 <=  Row 5 - Row 2
 
The entering variable is 2
 
The departing variable is 7 with feasibility ratio 3
 
  ERO: Row 1 <=  Row 1 / 2
  ERO: Row 2 <=  Row 2 - Row 1
  ERO: Row 3 <=  Row 3 - Row 1
  ERO: Row 4 <=  Row 4 - Row 1
  ERO: Row 5 <=  Row 5 + 3 Row 1
 
The objective changed from -10 to -1
 
The entering variable is 1
 
The departing variable is 8 with feasibility ratio 0.666667
 
  ERO: Row 2 <=  Row 2 / 1.50000
  ERO: Row 1 <=  Row 1 - 0.500000 Row 2
  ERO: Row 3 <=  Row 3 - 0.500000 Row 2
  ERO: Row 4 <=  Row 4 - 1.50000 Row 2
  ERO: Row 5 <=  Row 5 + 1.50000 Row 2
 
The objective changed from -1 to 0
 
Optimality test
 
 
Are all objective entries nonnegative?
 
Yes.  The current solution is optimal.
 
The linear programming solution:
 
               1           2           3           4           5           6
 
       0.6666667   2.6666667   0.0000000   0.0000000   1.6666667   4.0000000
 
               7           8
 
       0.0000000   0.0000000
 
Objective = 0
 
This problem has artificial variables.
Use the "V" command to remove them.
 
  The linear programming table:
 
                1            2            3            4            5
 
X2      0.0000000    1.0000000   -0.6666667    0.3333333    0.0000000
X1      1.0000000    0.0000000    0.3333333   -0.6666667    0.0000000
X5      0.0000000    0.0000000    0.3333333    0.3333333    1.0000000
X6      0.0000000    0.0000000    0.0000000    1.0000000    0.0000000
Obj2    0.0000000    0.0000000    0.0000000    0.0000000    0.0000000
Obj   -40.0000000  -30.0000000    0.0000000    0.0000000    0.0000000
 
                6            7            8            P            C
 
X2      0.0000000    0.6666667   -0.3333333    0.0000000    2.6666667
X1      0.0000000   -0.3333333    0.6666667    0.0000000    0.6666667
X5      0.0000000   -0.3333333   -0.3333333    0.0000000    1.6666667
X6      1.0000000    0.0000000   -1.0000000    0.0000000    4.0000000
Obj2    0.0000000    1.0000000    1.0000000    1.0000000    0.0000000
Obj     0.0000000    0.0000000    0.0000000    1.0000000    0.0000000
 
Enter command? ("H" for help)
 
All the artificial variables were deleted.
The original objective function is restored.
 
You must now use the "A" command to zero out
objective row entries for all basic variables.
 
  The linear programming table:
 
                1            2            3            4            5
 
X2      0.0000000    1.0000000   -0.6666667    0.3333333    0.0000000
X1      1.0000000    0.0000000    0.3333333   -0.6666667    0.0000000
X5      0.0000000    0.0000000    0.3333333    0.3333333    1.0000000
X6      0.0000000    0.0000000    0.0000000    1.0000000    0.0000000
Obj   -40.0000000  -30.0000000    0.0000000    0.0000000    0.0000000
 
                6            P            C
 
X2      0.0000000    0.0000000    2.6666667
X1      0.0000000    0.0000000    0.6666667
X5      0.0000000    0.0000000    1.6666667
X6      1.0000000    0.0000000    4.0000000
Obj     0.0000000    1.0000000    0.0000000
 
Enter command? ("H" for help)
  ERO: Row 5 <=  Row 5 + 40 Row 2
 
  The linear programming table:
 
                1            2            3            4            5
 
X2      0.0000000    1.0000000   -0.6666667    0.3333333    0.0000000
X1      1.0000000    0.0000000    0.3333333   -0.6666667    0.0000000
X5      0.0000000    0.0000000    0.3333333    0.3333333    1.0000000
X6      0.0000000    0.0000000    0.0000000    1.0000000    0.0000000
Obj     0.0000000  -30.0000000   13.3333333  -26.6666667    0.0000000
 
                6            P            C
 
X2      0.0000000    0.0000000    2.6666667
X1      0.0000000    0.0000000    0.6666667
X5      0.0000000    0.0000000    1.6666667
X6      1.0000000    0.0000000    4.0000000
Obj     0.0000000    1.0000000   26.6666667
 
Enter command? ("H" for help)
  ERO: Row 5 <=  Row 5 + 30 Row 1
 
  The linear programming table:
 
                 1             2             3             4             5
 
X2       0.0000000     1.0000000    -0.6666667     0.3333333     0.0000000
X1       1.0000000     0.0000000     0.3333333    -0.6666667     0.0000000
X5       0.0000000     0.0000000     0.3333333     0.3333333     1.0000000
X6       0.0000000     0.0000000     0.0000000     1.0000000     0.0000000
Obj      0.0000000     0.0000000    -6.6666667   -16.6666667     0.0000000
 
                 6             P             C
 
X2       0.0000000     0.0000000     2.6666667
X1       0.0000000     0.0000000     0.6666667
X5       0.0000000     0.0000000     1.6666667
X6       1.0000000     0.0000000     4.0000000
Obj      0.0000000     1.0000000   106.6666667
 
Enter command? ("H" for help)
 
The entering variable is 4
 
The departing variable is 6 with feasibility ratio 4
 
  ERO: Row 1 <=  Row 1 - 0.333333 Row 4
  ERO: Row 2 <=  Row 2 + 0.666667 Row 4
  ERO: Row 3 <=  Row 3 - 0.333333 Row 4
  ERO: Row 5 <=  Row 5 + 16.6667 Row 4
 
The objective changed from 106.667 to 173.333
 
The entering variable is 3
 
The departing variable is 5 with feasibility ratio 1.00000
 
  ERO: Row 3 <=  Row 3 / 0.333333
  ERO: Row 1 <=  Row 1 + 0.666667 Row 3
  ERO: Row 2 <=  Row 2 - 0.333333 Row 3
  ERO: Row 5 <=  Row 5 + 6.66667 Row 3
 
The objective changed from 173.333 to 180.000
 
Optimality test
 
 
Are all objective entries nonnegative?
 
Yes.  The current solution is optimal.
 
The linear programming solution:
 
               1           2           3           4           5           6
 
       3.0000000   2.0000000   1.0000000   4.0000000   0.0000000   0.0000000
 
Objective = 180.000
 
  The linear programming table:
 
                 1             2             3             4             5
 
X2       0.0000000     1.0000000     0.0000000     0.0000000     2.0000000
X1       1.0000000     0.0000000     0.0000000     0.0000000    -1.0000000
X3       0.0000000     0.0000000     1.0000000     0.0000000     3.0000000
X4       0.0000000     0.0000000     0.0000000     1.0000000     0.0000000
Obj      0.0000000     0.0000000     0.0000000     0.0000000    20.0000000
 
                 6             P             C
 
X2      -1.0000000     0.0000000     2.0000000
X1       1.0000000     0.0000000     3.0000000
X3      -1.0000000     0.0000000     1.0000000
X4       1.0000000     0.0000000     4.0000000
Obj     10.0000000     1.0000000   180.0000000
 
Enter command? ("H" for help)
 
  The linear programming table:
 
         1     2     3     4     5     6     P     C
 
X2       0     1     0     0     2    -1     0     2
X1       1     0     0     0    -1     1     0     3
X3       0     0     1     0     3    -1     0     1
X4       0     0     0     1     0     1     0     4
Obj      0     0     0     0    20    10     1   180
 
Enter command? ("H" for help)
 
The following examples are available:
  "S" a simple linear programming problem;
  "A" an advanced linear programming problem.
 
  "C" to cancel.
 
 
Advanced linear programming problem:
 
Maximize
  Z=40 X + 30 Y
subject to
  X + 2 Y > 6
2 X +   Y > 4
  X +   Y < 5
2 X +   Y < 8
 
 
  The linear programming table:
 
         1     2     3     4     5     6     7     8     P     C
 
X7       1     2    -1     0     0     0     1     0     0     6
X8       2     1     0    -1     0     0     0     1     0     4
X5       1     1     0     0     1     0     0     0     0     5
X6       2     1     0     0     0     1     0     0     0     8
Obj2     0     0     0     0     0     0     1     1     1     0
Obj    -40   -30     0     0     0     0     0     0     1     0
 
Enter command? ("H" for help)
 
The objective entry in column 7 is not zero,
but this corresponds to a basic variable.
 
  ERO: Row 5 <=  Row 5 - Row 1
 
The objective entry in column 8 is not zero,
but this corresponds to a basic variable.
 
  ERO: Row 5 <=  Row 5 - Row 2
 
The entering variable is 2
 
The departing variable is 7 with feasibility ratio 3
 
  ERO: Row 1 <=  Row 1 / 2
  ERO: Row 2 <=  Row 2 - Row 1
  ERO: Row 3 <=  Row 3 - Row 1
  ERO: Row 4 <=  Row 4 - Row 1
  ERO: Row 5 <=  Row 5 + 3 Row 1
 
The objective changed from -10 to -1
 
The entering variable is 1
 
The departing variable is 8 with feasibility ratio 0.666667
 
  ERO: Row 2 <=  Row 2 / 1.5
  ERO: Row 1 <=  Row 1 - 0.5 Row 2
  ERO: Row 3 <=  Row 3 - 0.5 Row 2
  ERO: Row 4 <=  Row 4 - 1.5 Row 2
  ERO: Row 5 <=  Row 5 + 1.5 Row 2
 
The objective changed from -1 to 0
 
The entering variable is 3
 
The departing variable is 1 with feasibility ratio 2.00030
 
  ERO: Row 2 <=  Row 2 / 0.3333
  ERO: Row 1 <=  Row 1 + 0.6666 Row 2
  ERO: Row 3 <=  Row 3 - 0.3334 Row 2
  ERO: Row 4 <=  Row 4 - 0.0001 Row 2
  ERO: Row 5 <=  Row 5 + 0.0001 Row 2
 
The objective changed from 0 to 0.0002
 
The entering variable is 4
 
The departing variable is 5 with feasibility ratio 0.999200
 
  ERO: Row 1 <=  Row 1 + 0.9997 Row 3
  ERO: Row 2 <=  Row 2 + 2 Row 3
  ERO: Row 4 <=  Row 4 - Row 3
  ERO: Row 5 <=  Row 5 + 0.0002 Row 3
 
The objective changed from 0.0002 to 0.0003998
 
Optimality test
 
 
Are all objective entries nonnegative?
 
Yes.  The current solution is optimal.
 
The linear programming solution:
 
            1        2        3        4        5        6        7        8
 
            0    4.997    3.998   0.9992        0    2.999        0        0
 
Objective = 0.0003998
 
This problem has artificial variables.
Use the "V" command to remove them.
 
  The linear programming table:
 
               1           2           3           4           5           6
 
X2        0.9993           1           0           0      0.9997           0
X3             1           0           1           0           2           0
X4            -1           0           0           1           1           0
X6        0.9997           0           0           0          -1           1
Obj2      0.0001           0           0           0      0.0002           0
Obj          -40         -30           0           0           0           0
 
               7           8           P           C
 
X2             0           0           0       4.997
X3            -1           0           0       3.998
X4             0          -1           0      0.9992
X6             0           0           0       2.999
Obj2      0.9999      0.9998           1   0.0003998
Obj            0           0           1           0
 
Enter command? ("H" for help)
The phase 1 objective function is nonzero.
Hence, this problem may have no solution.
 
All the artificial variables were deleted.
The original objective function is restored.
 
You must now use the "A" command to zero out
objective row entries for all basic variables.
 
  The linear programming table:
 
            1        2        3        4        5        6        P        C
 
X2     0.9993        1        0        0   0.9997        0        0    4.997
X3          1        0        1        0        2        0        0    3.998
X4         -1        0        0        1        1        0        0   0.9992
X6     0.9997        0        0        0       -1        1        0    2.999
Obj       -40      -30        0        0        0        0        1        0
 
Enter command? ("H" for help)
  ERO: Row 5 <=  Row 5 + 40 Row 2
 
  The linear programming table:
 
            1        2        3        4        5        6        P        C
 
X2     0.9993        1        0        0   0.9997        0        0    4.997
X3          1        0        1        0        2        0        0    3.998
X4         -1        0        0        1        1        0        0   0.9992
X6     0.9997        0        0        0       -1        1        0    2.999
Obj         0      -30       40        0       80        0        1    159.9
 
Enter command? ("H" for help)
  ERO: Row 5 <=  Row 5 + 30 Row 1
 
  The linear programming table:
 
            1        2        3        4        5        6        P        C
 
X2     0.9993        1        0        0   0.9997        0        0    4.997
X3          1        0        1        0        2        0        0    3.998
X4         -1        0        0        1        1        0        0   0.9992
X6     0.9997        0        0        0       -1        1        0    2.999
Obj     29.97        0       40        0    109.9        0        1    309.8
 
Enter command? ("H" for help)
 
The objective entry in column 3 is not zero,
but this corresponds to a basic variable.
 
  ERO: Row 5 <=  Row 5 - 40 Row 2
 
The entering variable is 1
 
The departing variable is 6 with feasibility ratio 2.99990
 
  ERO: Row 4 <=  Row 4 / 0.9997
  ERO: Row 1 <=  Row 1 - 0.9993 Row 4
  ERO: Row 2 <=  Row 2 - Row 4
  ERO: Row 3 <=  Row 3 + Row 4
  ERO: Row 5 <=  Row 5 + 10.03 Row 4
 
The objective changed from 149.9 to 179.9
 
Optimality test
 
 
Are all objective entries nonnegative?
 
Yes.  The current solution is optimal.
 
The linear programming solution:
 
           1       2       3       4       5       6
 
           3       2   0.998   3.999       0       0
 
Objective = 179.9
 
  The linear programming table:
 
             1         2         3         4         5         6         P
 
X2           0         1         0         0     1.999   -0.9993         0
X3           0         0         1         0         3        -1         0
X4           0         0         0         1         0         1         0
X1           1         0         0         0        -1         1         0
Obj          0         0         0         0     19.87     10.03         1
 
             C
 
X2           2
X3       0.998
X4       3.999
X1           3
Obj      179.9
 
Enter command? ("H" for help)
Closing the transcript file "output.txt".
 
Enter command? ("H" for help)
Enter "Y" to confirm you want to quit.
 
MATMAN():
  Normal end of execution.
26 October 2023   8:33:23.243 AM