# Strange result with GLPK

This program

%display latex
m=3
n=2
A=matrix(m,n,(0,1,1,0,6,18))
bmin=[12,0,70]
bmax=[oo,10,70]
c=matrix(1,n,(4.1,8))
show(A,bmin,bmax,c)

p = MixedIntegerLinearProgram(maximization=False, solver = "GLPK")
x = p.new_variable(integer=False, indices=[0..n-1]) # les nouvelles variables seront x... x}
B = A * x # m
for i in range(m):
for i in range(n):
p.set_min(x[i],0)
p.set_objective(4.1*x+8*x)
p.show()
p.set_min(x[i],0)


p.set_objective(4.1x+8x p.show() p.solve()

has obviously no solution as show by the result of

z=p.polyhedron()
zz=z.vertices()
zz


(There are no vertices)

but

p.solve()


gives 96 and

valeurs=p.get_values(x) valeurs

gives

${0:0.0,1:12.0}$

but $18 *12 =216 \geq 70$ wich shows the assertion

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Please format the posted question so that all code is displayed as code. I am also not respecting the pep8 guiding lines in typing code, but some touch for the readability should be present in the lines, else it is hard to digest. So please let there be some space before and after the equal sign in the definition of variables.

Hello, @Cyrille. This problem has no polyhedron, as far as I can understand. If you see the third constraint in your problem, you will notice it is an equality (bmin $=$ bmax), which makes its plot a line.

On the other hand, I am wondering how you got the result for p.solve(), since I get that the MILP has no feasible solution, as in my answer below.

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Hello, @Cyrille! I think you forgot to call p.solve(). It indicates me

MIPSolverException: GLPK: Problem has no feasible solution

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