#Zadatak 4

from cvxopt.glpk import ilp
from cvxopt import solvers
from cvxopt.base import matrix
import numpy as np
RealNumber=float
Integer=int
c1=matrix([-1. , -1.])
A=matrix([[-1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.],
[0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. , 0. , 0. , 0. , 0. , 0. , 0.],
[0. , 0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. , 0. , 0. , 0. , 0. , 0.],
[0. , 0. , 0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. , 0. ,0. , 0. , 0.],
[0. , 0. , 0. , 0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. ,0. , 0. , 0.],
[0. , 0. , 0. , 0. , 0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1. , 0. , 0. , 0.],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,1. , 0. , 0.],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,0. , 1. , 0.],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , -1. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 1.]])
h=matrix([0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 6. , 8. , 2. , 4. , 1. ,5. , 3. , 4. , 8. , 9.])
beq=matrix([0. , 0. , 0. , 0.])
Aeq=matrix([[1. , 0. , 0. , 0.],[0. , 1. , 0. , 0.],[-1. , 1. , 0. , 0.],[-1. , 0. , 1. , 0.],[-1. , 0. , 0. , 1.],[0. , -1. , 1. , 0.],[0. , -1. , 0. , 1.],[0. , 0. , 1. , -1.],[0. , 0. , -1. , 0.],[0. , 0. , 0. , -1.]])
(status, x1)=ilp(c1, A, h, Aeq, beq)
print x1