# NLP written by GAMS Convert at 02/17/22 17:22:54
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#         8        2        0        6        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#         4        4        0        0        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#        18       18        0
#
# Reformulation has removed 1 variable and 1 equation

from pyomo.environ import *

model = m = ConcreteModel()

m.x1 = Var(within=Reals, bounds=(-10,5), initialize=0)
m.x2 = Var(within=Reals, bounds=(-10,20), initialize=0)
m.x3 = Var(within=Reals, bounds=(None,None), initialize=0)
m.x4 = Var(within=Reals, bounds=(None,None), initialize=0)

m.obj = Objective(sense=minimize, expr= m.x3 * m.x4)

m.e1 = Constraint(expr= 2 * m.x1 + m.x2 <= 14)
m.e2 = Constraint(expr= m.x1 + m.x2 <= 10)
m.e3 = Constraint(expr= -4 * m.x1 + m.x2 <= 0)
m.e4 = Constraint(expr= -2 * m.x1 - m.x2 <= -6)
m.e5 = Constraint(expr= -m.x1 - 2 * m.x2 <= -6)
m.e6 = Constraint(expr= m.x1 - m.x2 <= 3)
m.e7 = Constraint(expr= m.x1 + m.x2 - m.x3 == 0)
m.e8 = Constraint(expr= m.x1 - m.x2 - m.x4 == -7)