import pyomo.environ as pyo
from pyomo.contrib import appsi

m = pyo.ConcreteModel()
m.x = pyo.Var(domain = pyo.Binary)
m.y = pyo.Var(domain = pyo.Binary)
m.fx = pyo.Var(domain = pyo.NonNegativeReals)
m.fy = pyo.Var(domain = pyo.NonNegativeReals)
m.c1 = pyo.Constraint(expr = m.fx <= m.x)
m.c2 = pyo.Constraint(expr = m.fy <= m.y)
m.c3 = pyo.Constraint(expr = m.x + m.y <= 1)

m.obj = pyo.Objective(
    expr = m.fx * 0.5 + m.fy * 0.4, 
    sense = pyo.maximize,
)

opt = appsi.solvers.Highs()
opt.config.load_solution = False
# opt.update_config.treat_fixed_vars_as_params = False

# solution 1 has m.x == 1 and m.y == 0
r = opt.solve(m)
print(r)
assert r.best_feasible_objective is not None

# solution 2 has m.x == 0 and m.y == 1
m.y.fix(1)
r = opt.solve(m)
print(r)
assert r.best_feasible_objective is not None

# solution 3 should be equal solution 1 but get infeasible
m.y.unfix()
m.x.fix(1)
r = opt.solve(m)
print(r)
assert r.best_feasible_objective is None