# ApCoCoA-1:GLPK.LPSolve

## GLPK.LPSolve

Solving linear programmes.

### Syntax

GLPK.LPSolve(Objective_f:POLY, EQ_Poly:LIST, LE_Poly:LIST, GE_Poly:LIST, Bounds:LIST, Method:STRING, MinMax: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

*EQ_Poly*: List of linear polynomials, which are equivalent to the equality-part in the list of conditions.@param

*LE_Poly*: List of linear polynomials, which are equivalent to the lower or equal-part in the list of conditions.@param

*GE_Poly*: List of linear polynomials, which are equivalent to the greater or equal-part in the list of conditions.@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.@param

*MinMax*: Minimization ("Min") or maximization ("Max"), that's the question.@return List of linear polynomials, the zeros of the polynomials are the points where the optimal value of the objective function is archieved

#### Example

-- We want to maximize the Function y = - 1/2x, -- with the two conditions y ≤ 6 - 3/4x and y ≥ 1 - x and the bounds 0 ≤ x ≤ 6 and 1/3 ≤ y ≤ 4. -- We prename the input of GLPK.LPSol-function. Use S::=Q[x,y]; OF := 1/2x + y; LE := [3/4x + y - 6]; GE := [x + y - 1]; Bounds:=[[0,6], [1/3,4]]; -- Then we compute the solution with $GLPK.LPSolve(OF, [], LE, GE, Bounds, "Simplex", "Max"); -- And we achieve: ------------------------------------- Solution Status: OPTIMAL Value of objective function: 5333333333/1000000000 [x[1] - 266667/100000, x[2] - 4]