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### qp.py

#!/usr/bin/python

# Copyright 2019, Gurobi Optimization, LLC

# This example formulates and solves the following simple QP model:
#  minimize
#      x^2 + x*y + y^2 + y*z + z^2 + 2 x
#  subject to
#      x + 2 y + 3 z >= 4
#      x +   y       >= 1
#      x, y, z non-negative
#
# It solves it once as a continuous model, and once as an integer model.

from gurobipy import *

# Create a new model
m = Model("qp")

# Create variables

# Set objective: x^2 + x*y + y^2 + y*z + z^2 + 2 x
obj = x*x + x*y + y*y + y*z + z*z + 2*x
m.setObjective(obj)

# Add constraint: x + 2 y + 3 z <= 4
m.addConstr(x + 2 * y + 3 * z >= 4, "c0")

# Add constraint: x + y >= 1
m.addConstr(x + y >= 1, "c1")

m.optimize()

for v in m.getVars():
print('%s %g' % (v.varName, v.x))

print('Obj: %g' % obj.getValue())

x.vType = GRB.INTEGER
y.vType = GRB.INTEGER
z.vType = GRB.INTEGER

m.optimize()

for v in m.getVars():
print('%s %g' % (v.varName, v.x))

print('Obj: %g' % obj.getValue())