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Hello everyone,

The following contains the
SIMPLEX METHOD (Linear Programming, Maximization)

Using material from
Frederick S. Hiller, Gerald J. Lieberman. Introduction to Operations Research. New York: McGraw Hill, 2005. Print.

Please let us know, if you would like us to include modifications, improvements, and any additions to the code.

Truly,

Haulwind Team

================================================== ===========
maximize Z,
where Z = C * X AND A * X ≤ b
where C,X, and b are vectors; and A is a Matrix
e.g. max Z; C1X1 + C2X2 = Z
A1X1+ A2X2 ≤ b1
A3X1+ A4X2 ≤ b2
A5X1+ A5X2 ≤ b3

================================================== ===========
INPUT
C = {C1, C2}= L1
b = {b1, b2,b3}= L2
A = [ A1 A2
A3 A4
A5 A6 ]
= [A]
OUTPUT
X = [X1 X2]= LE
Z = Z
================================================== ===========
DIM(L1) -> N
DIM(L2) -> M
{1,1} -> DIM[B]
0 -> DIM(L5)

-L1 -> L1
AUGMENT([A],IDENTITY[M]) -> [C]
1 -> K
WHILE L1(K) ≠ MIN(L1)
K+1 -> K
END

0 -> DIM(L4)
M -> DIM(L4)
0 -> DIM(L3)
0 -> DIM(L5)
0 -> DIM(LZ)
{1,1} -> DIM([B])
L2 -> LD
L1 -> LX

FOR (A,1,M,1)
A+N -> L3(A)
END

LBL 1
AUGMENT (-LX,L4) -> L6

0 -> DIM(LK)

FOR(Q,1,M,1)
IF [A](Q,K) ≠ 0
THEN
L2(Q)/[A](Q,K) -> LK(Q)
ELSE
MAX(L2) -> LK(Q)
END END

1 -> Y
FOR (Q,1,M,1)
IF [A](Q,K) ≠ 0
THEN
IF (L2(Q)/[A](Q,K)) = MIN(LK)
THEN
IF Y = 1
K -> L3(Q)
Y+1 -> Y
END END END END
{M,M} -> DIM([B])

FOR(A,1,M,1)
FOR(B,1,M,1)
[C](B,L3(A)) -> [B](B,A)
END END

[B]-1 -> [D]

FOR (A,1,M,1)
L6(L3(A)) -> L5(A)
END

L5 -> LZ
0 -> DIM(LC)
FOR(A,1,M,1)
FOR(B,1,M,1)
[D](A,B)*LD(B) -> L5(B)
END
SUM(L5) -> LC(A)
END

LC -> L2
N -> DIM(LE)
0 -> DIM(LF)

FOR(B,1,M,1)
FOR(A,1,M,1)
LZ(A)*[D](A,B) -> L5(A)
END
SUM(L5) -> LF(B)
END

0 -> DIM(LY)

FOR(B,1,N,1)
FOR(A,1,M,1)
LF(A)*[A](A,B) -> L5(A)
END
SUM(L5) -> LY(B)
END
LY + LX -> L1

IF MIN(L1)<0
THEN
1 -> K
WHILE L1(K) ≠ MIN (L1)
K+1 -> K
END
GOTO 1
END

SUM (LZ*L2) -> Z
DISP ''THE OPTIMAL SOLUTION IS''
DISP Z

FOR(A,1,M,1)
FOR(B,1,N,1)
IF L1(B) = 0
THEN
IF L3(A) = B
THEN
L2(A) -> LE(B)
END
ELSE
0 -> LE(B)
END END END
DISP ''THE OPTIMAL QUANTITY FOR EACH RESOURCE IS''
DISP LE

CLEARALLLISTS
================================================== ===========


All of the previous files are available in MS Word @
ticalc.org/archives/files/authors/110/11095.html

Finally, we planning on devling further in the Linear Programming algorithms, for operational and financial applications.

If you have specific requests, please let us know, specifically, if you prefer the programs to be dowloadable rather than the code being published, and whether you would like a user interface for those programs.

Truly,
Haulwind Team

haulwind.com
linkedin.com/company/haulwind
slideshare.net/haulwind

Still bored:
I've cleaned it up to be more readable, though I didn't recase some of the tokens properly. I've also optimized it for size.

Code:

Some tips on size-optimizing things:
* Remove all "s, }s, and )s before a newline or →
* Rearrange If statements to help remove a parenthesis at the end
* If X=0 becomes If not(X
* If statements return true for any value over zero. If X≠0 can be If X
* Avoid using X*Y, and instead use XY
* Rearrange statements to use less bytes, if possible
I've started to be able to produce code that follows these rules the first time around, it would be good for you to develop similar habits.