# Package glpk/GLPK.LPMin

This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1: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]