# NLP written by GAMS Convert at 02/17/22 17:19:05
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#         7        1        0        6        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#         5        5        0        0        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#        33        9       24
#
# 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=0.187)
m.x2 = Var(within=Reals, bounds=(1e-06,1), initialize=0.56)
m.x3 = Var(within=Reals, bounds=(1e-06,1), initialize=0.253)
m.x4 = Var(within=Reals, bounds=(40,90), initialize=72.957)
m.x5 = Var(within=Reals, bounds=(0,None), initialize=0)

m.obj = Objective(sense=minimize, expr= m.x5)

m.e1 = Constraint(expr= (0.549337520233386 * m.x2 + 1.1263896788319 * m.x3) / (
    m.x1 + 0.816722116903399 * m.x2 + 0.538540530229217 * m.x3) + (
    0.0910522583583458 * m.x2) / (0.972203312166101 * m.x1 + m.x2 +
    0.394821041898112 * m.x3) - (0.273994101407968 * m.x3) / (1.07810138009609
    * m.x1 + 0.707289137797622 * m.x2 + m.x3) + (-m.x1 * (0.549337520233386 *
    m.x2 + 1.1263896788319 * m.x3) / (m.x1 + 0.816722116903399 * m.x2 +
    0.538540530229217 * m.x3)**2) - 0.972203312166101 * m.x2 * (
    0.0910522583583458 * m.x1 + 1.03765878646318 * m.x3) / (0.972203312166101 *
    m.x1 + m.x2 + 0.394821041898112 * m.x3)**2 - 1.07810138009609 * m.x3 * (
    -0.273994101407968 * m.x1 + 0.692718766203089 * m.x2) / (1.07810138009609 *
    m.x1 + 0.707289137797622 * m.x2 + m.x3)**2 - 3667.70490156687 / (226.184
    + m.x4) - m.x5 <= -12.0457123581059)
m.e2 = Constraint(expr= (0.0910522583583458 * m.x1 + 1.03765878646318 * m.x3)
    / (0.972203312166101 * m.x1 + m.x2 + 0.394821041898112 * m.x3) + (
    0.549337520233386 * m.x1) / (m.x1 + 0.816722116903399 * m.x2 +
    0.538540530229217 * m.x3) + (0.692718766203089 * m.x3) / (1.07810138009609
    * m.x1 + 0.707289137797622 * m.x2 + m.x3) + (-0.816722116903399 * m.x1 * (
    0.549337520233386 * m.x2 + 1.1263896788319 * m.x3) / (m.x1 +
    0.816722116903399 * m.x2 + 0.538540530229217 * m.x3)**2) - m.x2 * (
    0.0910522583583458 * m.x1 + 1.03765878646318 * m.x3) / (0.972203312166101 *
    m.x1 + m.x2 + 0.394821041898112 * m.x3)**2 - 0.707289137797622 * m.x3 * (
    -0.273994101407968 * m.x1 + 0.692718766203089 * m.x2) / (1.07810138009609 *
    m.x1 + 0.707289137797622 * m.x2 + m.x3)**2 - 2904.34268119711 / (221.969
    + m.x4) - m.x5 <= -9.63112952618865)
m.e3 = Constraint(expr= (-0.273994101407968 * m.x1 + 0.692718766203089 * m.x2)
    / (1.07810138009609 * m.x1 + 0.707289137797622 * m.x2 + m.x3) + (
    1.1263896788319 * m.x1) / (m.x1 + 0.816722116903399 * m.x2 +
    0.538540530229217 * m.x3) + (1.03765878646318 * m.x2) / (0.972203312166101
    * m.x1 + m.x2 + 0.394821041898112 * m.x3) + (-0.538540530229217 * m.x1 * (
    0.549337520233386 * m.x2 + 1.1263896788319 * m.x3) / (m.x1 +
    0.816722116903399 * m.x2 + 0.538540530229217 * m.x3)**2) -
    0.394821041898112 * m.x2 * (0.0910522583583458 * m.x1 + 1.03765878646318 *
    m.x3) / (0.972203312166101 * m.x1 + m.x2 + 0.394821041898112 * m.x3)**2 -
    m.x3 * (-0.273994101407968 * m.x1 + 0.692718766203089 * m.x2) / (
    1.07810138009609 * m.x1 + 0.707289137797622 * m.x2 + m.x3)**2 -
    3984.92283948829 / (233.426 + m.x4) - m.x5 <= -11.9515596536534)
m.e4 = Constraint(expr= -(0.549337520233386 * m.x2 + 1.1263896788319 * m.x3) /
    (m.x1 + 0.816722116903399 * m.x2 + 0.538540530229217 * m.x3) - (
    0.0910522583583458 * m.x2) / (0.972203312166101 * m.x1 + m.x2 +
    0.394821041898112 * m.x3) + (0.273994101407968 * m.x3) / (1.07810138009609
    * m.x1 + 0.707289137797622 * m.x2 + m.x3) + m.x1 * (0.549337520233386 *
    m.x2 + 1.1263896788319 * m.x3) / (m.x1 + 0.816722116903399 * m.x2 +
    0.538540530229217 * m.x3)**2 + 0.972203312166101 * m.x2 * (
    0.0910522583583458 * m.x1 + 1.03765878646318 * m.x3) / (0.972203312166101 *
    m.x1 + m.x2 + 0.394821041898112 * m.x3)**2 + 1.07810138009609 * m.x3 * (
    -0.273994101407968 * m.x1 + 0.692718766203089 * m.x2) / (1.07810138009609 *
    m.x1 + 0.707289137797622 * m.x2 + m.x3)**2 + 3667.70490156687 / (226.184
    + m.x4) - m.x5 <= 12.0457123581059)
m.e5 = Constraint(expr= -(0.0910522583583458 * m.x1 + 1.03765878646318 * m.x3)
    / (0.972203312166101 * m.x1 + m.x2 + 0.394821041898112 * m.x3) - (
    0.549337520233386 * m.x1) / (m.x1 + 0.816722116903399 * m.x2 +
    0.538540530229217 * m.x3) - (0.692718766203089 * m.x3) / (1.07810138009609
    * m.x1 + 0.707289137797622 * m.x2 + m.x3) + 0.816722116903399 * m.x1 * (
    0.549337520233386 * m.x2 + 1.1263896788319 * m.x3) / (m.x1 +
    0.816722116903399 * m.x2 + 0.538540530229217 * m.x3)**2 + m.x2 * (
    0.0910522583583458 * m.x1 + 1.03765878646318 * m.x3) / (0.972203312166101 *
    m.x1 + m.x2 + 0.394821041898112 * m.x3)**2 + 0.707289137797622 * m.x3 * (
    -0.273994101407968 * m.x1 + 0.692718766203089 * m.x2) / (1.07810138009609 *
    m.x1 + 0.707289137797622 * m.x2 + m.x3)**2 + 2904.34268119711 / (221.969
    + m.x4) - m.x5 <= 9.63112952618865)
m.e6 = Constraint(expr= -(-0.273994101407968 * m.x1 + 0.692718766203089 * m.x2)
    / (1.07810138009609 * m.x1 + 0.707289137797622 * m.x2 + m.x3) - (
    1.1263896788319 * m.x1) / (m.x1 + 0.816722116903399 * m.x2 +
    0.538540530229217 * m.x3) - (1.03765878646318 * m.x2) / (0.972203312166101
    * m.x1 + m.x2 + 0.394821041898112 * m.x3) + 0.538540530229217 * m.x1 * (
    0.549337520233386 * m.x2 + 1.1263896788319 * m.x3) / (m.x1 +
    0.816722116903399 * m.x2 + 0.538540530229217 * m.x3)**2 + 0.394821041898112
    * m.x2 * (0.0910522583583458 * m.x1 + 1.03765878646318 * m.x3) / (
    0.972203312166101 * m.x1 + m.x2 + 0.394821041898112 * m.x3)**2 + m.x3 * (
    -0.273994101407968 * m.x1 + 0.692718766203089 * m.x2) / (1.07810138009609 *
    m.x1 + 0.707289137797622 * m.x2 + m.x3)**2 + 3984.92283948829 / (233.426
    + m.x4) - m.x5 <= 11.9515596536534)
m.e7 = Constraint(expr= m.x1 + m.x2 + m.x3 == 1)