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Linear
Programming (revised simplex), proper form
Solves an LP problem in standard form by the
rev. simplex, in proper form. |
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| Problem |
Case 3 — Bronson 4.19; z*min = 270, x = (30 0 30 20) |
| Optimization |
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Maximization or minimization. • |
| c |
Coefficients in the objective function,
z = c x .
|
• Decimal mark: American (.) or European (,)
• Separation by: blanks, (Excel type) tabs. • |
A | b
(m×n,
m×1) |
Constraints, A x = b
(m equality constraints)
|
• Decimal mark & separation: as above
• Insert only:
row(1), b(1)
[:row(i), b(i), i = 2..m]
• Identity matrix: inserted by program
(':' = 'new line') • |
| Artificial variables |
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Which artificial variables (0 if none). • |
| Big M |
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Big M (∞), ignored if unnecessary. • |
| First graph basis |
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First basis for graph (avoiding artificials). • |
| Show values ? |
Test: (0, 1, 2) |
Shows the coordinates of the graph; & test level. • |
Solves a Linear Programming problem
supplied by the user in standard form, by Dantzig's
simplex method in the revised simplex (i.e., matrix) form.
In the standard form here: all the constraints must be given
as equations, after insertion of surplus
variables (if appropriate);
and with non-negative right-hand side constants,
i.e., b ≥ 0.
If any artificial variable is declared, its coefficient
will be (automatically) made ±M, according to the direction
of optimization ('+' for min, '−' for max).
Base problem is: Case 3 — Bronson 4.19; z*min = 270, x = (30 0 30 20)
 Other data.pdf (adequate to this webpage), Ramalhete.xlsx,
lp_diet
.txt,
.lp,
.xlsx
A plot of the objective function, z, is presented
as a function of the successive bases.
The initial basis is № 0. |
| References: |
Plate: LP_revised3 |
• Wikipedia: Revised simplex method.
Decimal mark
• Google: "revised simplex method"
• 1811-03-11: Le Verrier, Urbain Jean Joseph
(1887-09-23). |
