Simplex Algorithm

[ftneek]

Ok, your change to sol() don't seem to change the output of simplex2() (on the examples from the thread that I tried), so I think I will accept it.

Also, I misspoke earlier. Before, the 15/7 effected the primal solution (though it does not really matter as it is an artificial variable, they usually end up being 0). What matters for the Dual solution is the values of the final c row.

In short, for this example:
Min -> Max
2 "=" constraints -> y1,y2 unrestricted
x1,x2,x3>=0 -> 3 "<=" constraints
Constant terms of constraints -> Objective function coefficients
Objective function coefficients -> Constraint terms of constraints
Constraint coefficients matrix A^t -> A

Quote:Solving a minimization problem containing equality constraints, a sign change adjustment is necessary when determining an optimal solution point to the dual. The value of each unrestricted variable in the optimal solution point to the dual is the negative of the entry in the bottom row of the associated artificial variable column. (Because for a maximization problem, the corresponding minimization problem is considered, which necessitates an initial sign change in the objective function coefficients when entered in to the initial tableau.)

Thus y1=2/7,y2=-10/7 is the solution to the associated dual maximization problem. Negative solutions are valid, since y2 is unrestricted. This is generally relevant and important information for price analysis and business related questions.

When I get around to it (busy today), I think it would be helpful to compile some test cases of the examples shared on the forum so far. Any proposed changes to the code base should not affect the output of simplex2() with correct arguments.