will select the dual simplex method. It does not give you the dual solution per se. (To be precise: afterwards you can retrieve both the primal and dual solution).

The way to retrieve the solution after solving is:

If all variables (structural and logical) are non-negative (i.e. x>=0 and slacks s>=0) then all non-basic variables are equal to zero. As they are fixed to zero we only have to solve for the m basic variables.

Essentially we have to solve

A x = b

Unfortunately this is a non-square system of equations (after adding slacks we always have more columns than rows). In LPs we can form a basic solution and partition this into

B x_B + N x_N = b

After setting x_N = 0 we have just a square system of linear equations with solution:

x_B = inv(B) b

There is a fundamental theorem that says we can restrict the search to only basic solutions i.e. solutions that can be partitioned in basic and non-basic variables

x = [ x_B ]
[ x_N ]

with x_B >= 0 and x_N = 0.

For more info open a book about Linear Programming; a very good one is Vanderbei.

The line

will select the dual simplex method. It does not give you the dual solution per se. (To be precise: afterwards you can retrieve both the primal and dual solution).

The way to retrieve the solution after solving is:

Remember in linear programming

are all different things. For more information please consult a book on Linear Programming (e.g. Vanderbei).

If all variables (structural and logical) are non-negative (i.e.

`x>=0`

and slacks`s>=0`

) then all non-basic variables are equal to zero. As they are fixed to zero we only have to solve for the`m`

basic variables.Essentially we have to solve

Unfortunately this is a non-square system of equations (after adding slacks we always have more columns than rows). In LPs we can form a basic solution and partition this into

After setting

`x_N = 0`

we have just a square system of linear equations with solution:There is a fundamental theorem that says we can restrict the search to only basic solutions i.e. solutions that can be partitioned in basic and non-basic variables

with

`x_B >= 0`

and`x_N = 0`

.For more info open a book about Linear Programming; a very good one is Vanderbei.