# NLP written by GAMS Convert at 02/17/22 17:19:06
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#         9        1        0        8        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#         6        6        0        0        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#        52       12       40
#
# Reformulation has removed 1 variable and 1 equation

from pyomo.environ import *

model = m = ConcreteModel()

m.x1 = Var(within=Reals, bounds=(1e-06,1), initialize=0.322)
m.x2 = Var(within=Reals, bounds=(1e-06,1), initialize=0.322)
m.x3 = Var(within=Reals, bounds=(1e-06,1), initialize=0.222)
m.x4 = Var(within=Reals, bounds=(1e-06,1), initialize=0.133)
m.x5 = Var(within=Reals, bounds=(40,90), initialize=63.558)
m.x6 = Var(within=Reals, bounds=(0,None), initialize=0)

m.obj = Objective(sense=minimize, expr= m.x6)

m.e1 = Constraint(expr= 8.85 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 +
    4.5 * m.x4) - 9.85 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86 *
    m.x4) - (-0.865100000000001 * m.x1 + 3.8613 * m.x2 + 3.7136 * m.x3 -
    0.632999999999999 * m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5
    * m.x4) - 0.92 * log(0.92 * m.x1 + 0.074630773041249 * m.x2 +
    0.120222883700913 * m.x3 + 0.161199992780481 * m.x4) + 0.92 * log(0.92 *
    m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86 * m.x4) - 0.92 * (0.92 * m.x1 / (
    0.92 * m.x1 + 0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 +
    0.161199992780481 * m.x4) + (5.42978509857797 * m.x2) / (1.65960208993081 *
    m.x1 + 3.01 * m.x2 + 2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) +
    (3.53361528312402 * m.x3) / (1.35455252519754 * m.x1 + 1.86011323009376 *
    m.x2 + 2.4 * m.x3 + 2.64991431773289 * m.x4) + (5.92791255201582 * m.x4) /
    (1.41287034918512 * m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3
    + 3.86 * m.x4)) - 3803.98 / (231.47 + m.x5) - m.x6 <= -12.8590236275375)
m.e2 = Constraint(expr= 14.05 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 +
    4.5 * m.x4) - 15.05 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86 *
    m.x4) - (-1.6277 * m.x1 + 7.26510000000001 * m.x2 + 6.9872 * m.x3 - 1.191 *
    m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 * m.x4) - 3.01 *
    log(1.65960208993081 * m.x1 + 3.01 * m.x2 + 2.91963915785291 * m.x3 +
    1.70144966342223 * m.x4) + 3.01 * log(0.92 * m.x1 + 3.01 * m.x2 + 2.4 *
    m.x3 + 3.86 * m.x4) - 3.01 * (0.0228107346172588 * m.x1 / (0.92 * m.x1 +
    0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 + 0.161199992780481 *
    m.x4) + (3.01 * m.x2) / (1.65960208993081 * m.x1 + 3.01 * m.x2 +
    2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) + (1.48314676153655 *
    m.x3) / (1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4 * m.x3 +
    2.64991431773289 * m.x4) + (7.51049429784342 * m.x4) / (1.41287034918512 *
    m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3 + 3.86 * m.x4)) -
    2735.58621973158 / (226.276 + m.x5) - m.x6 <= -11.2296864040814)
m.e3 = Constraint(expr= 11 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5
    * m.x4) - 12 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86 * m.x4) -
    (-1.3079 * m.x1 + 5.83770000000001 * m.x2 + 5.6144 * m.x3 -
    0.956999999999998 * m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5
    * m.x4) - 2.4 * log(1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4
    * m.x3 + 2.64991431773289 * m.x4) + 2.4 * log(0.92 * m.x1 + 3.01 * m.x2 +
    2.4 * m.x3 + 3.86 * m.x4) - 2.4 * (0.0460854387520165 * m.x1 / (0.92 * m.x1
    + 0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 + 0.161199992780481
    * m.x4) + (3.66171411047386 * m.x2) / (1.65960208993081 * m.x1 + 3.01 *
    m.x2 + 2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) + (2.4 * m.x3) /
    (1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4 * m.x3 +
    2.64991431773289 * m.x4) + (4.17479603222384 * m.x4) / (1.41287034918512 *
    m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3 + 3.86 * m.x4)) -
    2788.51 / (220.79 + m.x5) - m.x6 <= -11.1728763302021)
m.e4 = Constraint(expr= 18.3 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 +
    4.5 * m.x4) - 19.3 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86 *
    m.x4) - (-1.845 * m.x1 + 8.23500000000001 * m.x2 + 7.92 * m.x3 - 1.35 *
    m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 * m.x4) - 3.86 * log
    (1.41287034918512 * m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3
    + 3.86 * m.x4) + 3.86 * log(0.92 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86
    * m.x4) - 3.86 * (0.0384207236678868 * m.x1 / (0.92 * m.x1 +
    0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 + 0.161199992780481 *
    m.x4) + (1.32677810541474 * m.x2) / (1.65960208993081 * m.x1 + 3.01 * m.x2
    + 2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) + (1.64761511983392 *
    m.x3) / (1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4 * m.x3 +
    2.64991431773289 * m.x4) + (3.86 * m.x4) / (1.41287034918512 * m.x1 +
    5.85662897318878 * m.x2 + 2.5957281029371 * m.x3 + 3.86 * m.x4)) -
    2739.24733002944 / (226.28 + m.x5) - m.x6 <= -11.3821403387577)
m.e5 = Constraint(expr= 9.85 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 +
    3.86 * m.x4) - 8.85 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 *
    m.x4) + (-0.865100000000001 * m.x1 + 3.8613 * m.x2 + 3.7136 * m.x3 -
    0.632999999999999 * m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5
    * m.x4) + 0.92 * log(0.92 * m.x1 + 0.074630773041249 * m.x2 +
    0.120222883700913 * m.x3 + 0.161199992780481 * m.x4) - 0.92 * log(0.92 *
    m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86 * m.x4) + 0.92 * (0.92 * m.x1 / (
    0.92 * m.x1 + 0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 +
    0.161199992780481 * m.x4) + (5.42978509857797 * m.x2) / (1.65960208993081 *
    m.x1 + 3.01 * m.x2 + 2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) +
    (3.53361528312402 * m.x3) / (1.35455252519754 * m.x1 + 1.86011323009376 *
    m.x2 + 2.4 * m.x3 + 2.64991431773289 * m.x4) + (5.92791255201582 * m.x4) /
    (1.41287034918512 * m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3
    + 3.86 * m.x4)) + 3803.98 / (231.47 + m.x5) - m.x6 <= 12.8590236275375)
m.e6 = Constraint(expr= 15.05 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 +
    3.86 * m.x4) - 14.05 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 *
    m.x4) + (-1.6277 * m.x1 + 7.26510000000001 * m.x2 + 6.9872 * m.x3 - 1.191 *
    m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 * m.x4) + 3.01 *
    log(1.65960208993081 * m.x1 + 3.01 * m.x2 + 2.91963915785291 * m.x3 +
    1.70144966342223 * m.x4) - 3.01 * log(0.92 * m.x1 + 3.01 * m.x2 + 2.4 *
    m.x3 + 3.86 * m.x4) + 3.01 * (0.0228107346172588 * m.x1 / (0.92 * m.x1 +
    0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 + 0.161199992780481 *
    m.x4) + (3.01 * m.x2) / (1.65960208993081 * m.x1 + 3.01 * m.x2 +
    2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) + (1.48314676153655 *
    m.x3) / (1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4 * m.x3 +
    2.64991431773289 * m.x4) + (7.51049429784342 * m.x4) / (1.41287034918512 *
    m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3 + 3.86 * m.x4)) +
    2735.58621973158 / (226.276 + m.x5) - m.x6 <= 11.2296864040814)
m.e7 = Constraint(expr= 12 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86
    * m.x4) - 11 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 * m.x4) +
    (-1.3079 * m.x1 + 5.83770000000001 * m.x2 + 5.6144 * m.x3 -
    0.956999999999998 * m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5
    * m.x4) + 2.4 * log(1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4
    * m.x3 + 2.64991431773289 * m.x4) - 2.4 * log(0.92 * m.x1 + 3.01 * m.x2 +
    2.4 * m.x3 + 3.86 * m.x4) + 2.4 * (0.0460854387520165 * m.x1 / (0.92 * m.x1
    + 0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 + 0.161199992780481
    * m.x4) + (3.66171411047386 * m.x2) / (1.65960208993081 * m.x1 + 3.01 *
    m.x2 + 2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) + (2.4 * m.x3) /
    (1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4 * m.x3 +
    2.64991431773289 * m.x4) + (4.17479603222384 * m.x4) / (1.41287034918512 *
    m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3 + 3.86 * m.x4)) +
    2788.51 / (220.79 + m.x5) - m.x6 <= 11.1728763302021)
m.e8 = Constraint(expr= 19.3 * log(1.97 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 +
    3.86 * m.x4) - 18.3 * log(2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 *
    m.x4) + (-1.845 * m.x1 + 8.23500000000001 * m.x2 + 7.92 * m.x3 - 1.35 *
    m.x4) / (2.11 * m.x1 + 3.97 * m.x2 + 3.19 * m.x3 + 4.5 * m.x4) + 3.86 * log
    (1.41287034918512 * m.x1 + 5.85662897318878 * m.x2 + 2.5957281029371 * m.x3
    + 3.86 * m.x4) - 3.86 * log(0.92 * m.x1 + 3.01 * m.x2 + 2.4 * m.x3 + 3.86
    * m.x4) + 3.86 * (0.0384207236678868 * m.x1 / (0.92 * m.x1 +
    0.074630773041249 * m.x2 + 0.120222883700913 * m.x3 + 0.161199992780481 *
    m.x4) + (1.32677810541474 * m.x2) / (1.65960208993081 * m.x1 + 3.01 * m.x2
    + 2.91963915785291 * m.x3 + 1.70144966342223 * m.x4) + (1.64761511983392 *
    m.x3) / (1.35455252519754 * m.x1 + 1.86011323009376 * m.x2 + 2.4 * m.x3 +
    2.64991431773289 * m.x4) + (3.86 * m.x4) / (1.41287034918512 * m.x1 +
    5.85662897318878 * m.x2 + 2.5957281029371 * m.x3 + 3.86 * m.x4)) +
    2739.24733002944 / (226.28 + m.x5) - m.x6 <= 11.3821403387577)
m.e9 = Constraint(expr= m.x1 + m.x2 + m.x3 + m.x4 == 1)