# NLP written by GAMS Convert at 02/17/22 17:19:07
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#        13       13        0        0        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#        16       16        0        0        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#        38       24       14
#
# Reformulation has removed 1 variable and 1 equation

from pyomo.environ import *

model = m = ConcreteModel()

m.x1 = Var(within=Reals, bounds=(10,350), initialize=10)
m.x2 = Var(within=Reals, bounds=(10,350), initialize=10)
m.x3 = Var(within=Reals, bounds=(10,200), initialize=10)
m.x4 = Var(within=Reals, bounds=(10,200), initialize=10)
m.x5 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x6 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x7 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x8 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x9 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x10 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x11 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x12 = Var(within=Reals, bounds=(0,10), initialize=0)
m.x13 = Var(within=Reals, bounds=(150,310), initialize=150)
m.x14 = Var(within=Reals, bounds=(150,310), initialize=150)
m.x15 = Var(within=Reals, bounds=(150,310), initialize=150)
m.x16 = Var(within=Reals, bounds=(150,310), initialize=150)

m.obj = Objective(sense=minimize, expr= 1300 * (1000 / (0.0333333333333333 *
    m.x1 * m.x2 + 0.166666666666667 * m.x1 + 0.166666666666667 * m.x2))**0.6 +
    1300 * (600 / (0.0333333333333333 * m.x3 * m.x4 + 0.166666666666667 * m.x3
    + 0.166666666666667 * m.x4))**0.6)

m.e1 = Constraint(expr= m.x5 + m.x9 == 10)
m.e2 = Constraint(expr= m.x5 - m.x6 + m.x11 == 0)
m.e3 = Constraint(expr= m.x7 + m.x9 - m.x10 == 0)
m.e4 = Constraint(expr= -m.x6 + m.x7 + m.x8 == 0)
m.e5 = Constraint(expr= -m.x10 + m.x11 + m.x12 == 0)
m.e6 = Constraint(expr= m.x16 * m.x11 - m.x13 * m.x6 + 150 * m.x5 == 0)
m.e7 = Constraint(expr= m.x15 * m.x7 - m.x14 * m.x10 + 150 * m.x9 == 0)
m.e8 = Constraint(expr= m.x6 * m.x15 - m.x6 * m.x13 == 1000)
m.e9 = Constraint(expr= m.x10 * m.x16 - m.x10 * m.x14 == 600)
m.e10 = Constraint(expr= m.x1 + m.x15 == 500)
m.e11 = Constraint(expr= m.x2 + m.x13 == 250)
m.e12 = Constraint(expr= m.x3 + m.x16 == 350)
m.e13 = Constraint(expr= m.x4 + m.x14 == 200)