Implementation of Simplex algorithm with Lexicographical minimum ratio test and Intiger pivoting for minimization. Solves linear problems of the form LP>=

Inputs:
A: m x n matrix of inequalities (>=)
a: m x 1 right hand side
c: optimization function

Outputs:
x: best feasible solution
cx: cost of the solution due to c
y: solution of the dual problem

Implementation of the Branch & Bound algorithm for Integer Linear Programming.

Inputs:
A: m x n matrix of inequalities (>=)
a: m x 1 right hand side
c: optimization function

Outputs:
x: best integer solution cx: cost of the integer solution due to c

lp_inequalities: converts a LPG problem in a LP problem with inequalities
lp_equalities: converts a LPG problem in a LP problem with equalities