Simplex method in prime how to use the constrains maximise s.t. constraints.

[Gil]

How long does it take to solve
This simplex system?

[ 0 0 1 0 'F' 0 ]
[ 0 0 0 1 'F' 0 ]
[ 4 4 3 7 'L' 90 ]
[ 6 3 5 4 'L' 120 ]
[ 5 2 3 3 'L' 60 ]
[ 0 1 0 0 'L' 15 ]
[ 1 0 0 0 'L' 10 ]
[ 6 5 1 2 'L' 100 ]
[ 75 65 80 75 0 'Max' ]]

L=less or equal
F=Free variable, here x3 and x4
G=Greater or equal

And for that one?
[[ 4 4 3 7 'L' 90 ]
[ 6 3 5 4 'L' 120 ]
[ 5 2 3 3 'L' 60 ]
[ 0 1 0 0 'L' 15 ]
[ 1 0 0 0 'L' 10 ]
[ 6 5 1 2 'L' 100 ]
[ 75 65 80 75 0 'Max' ]]

And the following special system

{
[[ 1 -1 1 -1 0 'E' 2 ]
[ 2 -2 -1 0 1 'E' 0 ]
[ 1 -1 3 0 0 0 'Min' ]]
{ Var†5¦Steps†10 Time†4¦s :

{ "[[ 1 -1 1 -1 0 'E' 2 ]
[ 2 -2 -1 0 1 'E' 0 ]
[ 1 -1 3 0 0 0 'Min' ]]" "{ Var\\|>5\\166Steps\\|>10 Time\\|>4\\166s :


Z-Min
: [ '14/3' 4.66666666667 ] :x1: [ '2/3' .666666666667 ] :x2: 0 :x3: [ '4/3' 1.33333333333 ] :x4: 0 :x5: 0 :
Or not? SIMPLEX 
Sol 
i: [ '2/3' 0 '4/3' 0 0 ] :
+\\Gm

[
\\>=0
]
*
d
, 
d
: [ 1 1 0 0 0 ] :
\\->Mixed 
Solution
:
 
0\\<=
\\Gl
\\<=1

\\Gl
(
Sol 1
) 
+
 (
1-\\Gl
) *
(not? SIMPLEX 
Sol 2
): Plus :
\\Gm

[
\\>=0
]
*
d
, 
d
: [ 1 1 0 0 0 ] }"

And
{
[[ 1 -1 0 0 1 0 0 'E' 3 ]
[ -3 2 9 2 0 -2 0 'E' 22 ]
[ 0 1 0 0 0 -1 0 'E' 2 ]
[ 4 3 5 0 1 0 -1 'E' 4 ]
[ -1 0 3 -1 0 0 0 0 'Max' ]]
{ :
S
 = \\GS(
\\Gl
i*
Sol 
i): with :0\\<=
\\Gl
i\\<=: 1 :\\GS
\\Gl
: 1 :
Main 
Sol 1
,as Zrow=
0
: in.Col\\1661\\166final.STEPS Var\\|>7\\166Steps\\|>15 Time\\|>8\\166s :


Z-Max
: 6 :x1: 0 :x2: 2 :x3: 2 :x4: 0 :x5: 5 :x6: 0 :x7: 17 :
Main 
Sol 2
,as Zrow=
0
: inCol\\1661\\166addit.STEPS Var\\|>7\\166Steps\\|>16 Time\\|>10\\166s :


Z-Max
: 6 :x1: 5 :x2: 2 :x3: [ '11/3' 3.66666666667 ] :x4: 0 :x5: 0 :x6: 0 :x7: [ '121/3' 40.3333333333 ] :
Or not? SIMPLEX 
Sol 
i: { [ 5 2 '11/3' 0 0 0 '121/3' ] [ 0 2 2 0 5 0 17 ] } :
+\\Gm
12
[
\\>=0
]
*
d
, 
d
: { [ 1 1 '1/3' 0 0 1 '26/3' ] [ 0 1 0 0 1 1 4 ] } :
\\->Mixed 
Solution
:
 
0\\<=
\\Gl
\\<=1

\\Gl
(
Sol 1
) 
+
 (
1-\\Gl
) *
(not? SIMPLEX 
Sol 2
): Plus :
\\Gm
12
[
\\>=0
]
*
d
, 
d
: { [ 1 1 '1/3' 0 0 1 '26/3' ] [ 0 1 0 0 1 1 4 ] } }" }