# Package glpk/GLPK.LPMin

## GLPK.LPMin

Solving linear programmes by minimizing the objective function.

### Syntax

```GLPK.LPMin(Objective_f:POLY, Inequations:LIST, Bounds:LIST, Method:STRING) :LIST
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

• @param Objective_f: A linear polynomial which is equivalent to the linear objective function.

• @param Inequations: List of linear polynomials, which are equivalent to the conditions of the linear program of the form A <= 0.

• @param Bounds: List of lists with two elements. Each List contains the lower and upper bounds for each variable. You can choose between INT or RAT for the type of each bound, if you type in a (empty) string, then it means minus infinity (first place) or plus infinity (second place).

• @param Method: You can choose between the interior-point-method ("InterP") or the simplex-algorithm ("Simplex"). Usually you should use the simplex-algorithm.

• @return List of linear polynomials, the zeros of the polynomials are the points where the optimal value of the objective function is achieved

#### Example

```Use S ::= QQ[x,y];
OF := (1/2)*x + y;
IE := [(3/4)*x + y - 6, -x - y + 1];
Bounds := [[0,6], [1/3,4]];
GLPK.LPMin(OF, IE, Bounds, "Simplex");
-- [666667/1000000,  333333/1000000]
```