```json
{
  "sym_variables": [
    ("x0", "security onions"),
    ("x1", "automatic alerts"),
    ("x2", "network administrators"),
    ("x3", "SOC operators"),
    ("x4", "honeypots"),
    ("x5", "deployed decoys"),
    ("x6", "patches per day")
  ],
  "objective_function": "2.94 * x0 + 9.55 * x1 + 4.4 * x2 + 7.52 * x3 + 9.96 * x4 + 4.12 * x5 + 7.42 * x6",
  "constraints": [
    "5.55 * x0 + 5.44 * x1 + 0.37 * x2 + 6.6 * x3 + 3.38 * x4 + 2.14 * x5 + 1.9 * x6 <= 259",
    "0.37 * x2 + 2.14 * x5 >= 17",
    "5.44 * x1 + 0.37 * x2 >= 24",
    "6.6 * x3 + 2.14 * x5 >= 32",
    "5.55 * x0 + 5.44 * x1 >= 24",
    "5.55 * x0 + 3.38 * x4 + 2.14 * x5 >= 33",
    "0.37 * x2 + 6.6 * x3 + 3.38 * x4 >= 33",
    "0.37 * x2 + 2.14 * x5 + 1.9 * x6 >= 33",
    "6.6 * x3 + 3.38 * x4 + 2.14 * x5 >= 33",
    "5.44 * x1 + 6.6 * x3 + 3.38 * x4 >= 33",
    "5.44 * x1 + 6.6 * x3 + 2.14 * x5 >= 33",
    "0.37 * x2 + 6.6 * x3 + 1.9 * x6 >= 33",
    "5.55 * x0 + 5.44 * x1 + 0.37 * x2 >= 33",
    "5.55 * x0 + 5.44 * x1 + 3.38 * x4 >= 33",
    "5.55 * x0 + 6.6 * x3 + 1.9 * x6 >= 33",
    "5.55 * x0 + 0.37 * x2 + 1.9 * x6 >= 33",
    "5.44 * x1 + 0.37 * x2 + 6.6 * x3 >= 33",
    "5.55 * x0 + 0.37 * x2 + 3.38 * x4 >= 33",
    "5.55 * x0 + 0.37 * x2 + 6.6 * x3 >= 33",
    "5.55 * x0 + 5.44 * x1 + 6.6 * x3 >= 33",
    "6.6 * x3 + 3.38 * x4 + 1.9 * x6 >= 33",
    "5.44 * x1 + 0.37 * x2 + 2.14 * x5 >= 33",
    "0.37 * x2 + 3.38 * x4 + 1.9 * x6 >= 33",
    "5.55 * x0 + 3.38 * x4 + 2.14 * x5 >= 24",
    "-1 * x1 + 4 * x6 >= 0",
    "5.44 * x1 + 0.37 * x2 + 3.38 * x4 <= 160",
    "3.38 * x4 + 2.14 * x5 + 1.9 * x6 <= 50",
    "5.55 * x0 + 0.37 * x2 + 1.9 * x6 <= 116",
    "5.55 * x0 + 6.6 * x3 + 2.14 * x5 <= 203",
    "5.44 * x1 + 6.6 * x3 + 1.9 * x6 <= 241",
    "5.44 * x1 + 2.14 * x5 + 1.9 * x6 <= 259",
    "0.37 * x2 + 6.6 * x3 + 3.38 * x4 <= 88",
    "5.55 * x0 + 5.44 * x1 + 0.37 * x2 <= 211",
    "5.55 * x0 + 6.6 * x3 + 3.38 * x4 <= 177",
    "5.44 * x1 + 3.38 * x4 + 1.9 * x6 <= 201",
    "0.37 * x2 + 6.6 * x3 + 2.14 * x5 <= 80",
    "x0, x1, x2, x3, x4, x5, x6 are integers"

    
  ]
}
```

```python
from gurobipy import Model, GRB

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

# Create variables
variables = {
    'security onions': m.addVar(vtype=GRB.INTEGER, name='security_onions'),
    'automatic alerts': m.addVar(vtype=GRB.INTEGER, name='automatic_alerts'),
    'network administrators': m.addVar(vtype=GRB.INTEGER, name='network_administrators'),
    'SOC operators': m.addVar(vtype=GRB.INTEGER, name='SOC_operators'),
    'honeypots': m.addVar(vtype=GRB.INTEGER, name='honeypots'),
    'deployed decoys': m.addVar(vtype=GRB.INTEGER, name='deployed_decoys'),
    'patches per day': m.addVar(vtype=GRB.INTEGER, name='patches_per_day')
}


# Set objective function
m.setObjective(2.94 * variables['security onions'] + 9.55 * variables['automatic alerts'] + 4.4 * variables['network administrators'] + 7.52 * variables['SOC operators'] + 9.96 * variables['honeypots'] + 4.12 * variables['deployed decoys'] + 7.42 * variables['patches per day'], GRB.MINIMIZE)

# Add constraints
impact = {'security onions': 5.55, 'automatic alerts': 5.44, 'network administrators': 0.37, 'SOC operators': 6.6, 'honeypots': 3.38, 'deployed decoys': 2.14, 'patches per day': 1.9}

m.addConstr(sum([impact[var_name] * variables[var_name] for var_name in impact]) <= 259, "r0_upper_bound")


constraints_vars = [
    (['network administrators', 'deployed decoys'], 17),
    (['automatic alerts', 'network administrators'], 24),
    (['SOC operators', 'deployed decoys'], 32),
    (['security onions', 'automatic alerts'], 24),
    (['security onions', 'honeypots', 'deployed decoys'], 33),
    (['network administrators', 'SOC operators', 'honeypots'], 33),
    (['network administrators', 'deployed decoys', 'patches per day'], 33),
    (['SOC operators', 'honeypots', 'deployed decoys'], 33),
    (['automatic alerts', 'SOC operators', 'honeypots'], 33),
    (['automatic alerts', 'SOC operators', 'deployed decoys'], 33),
    (['network administrators', 'SOC operators', 'patches per day'], 33),
    (['security onions', 'automatic alerts', 'network administrators'], 33),
    (['security onions', 'automatic alerts', 'honeypots'], 33),
    (['security onions', 'SOC operators', 'patches per day'], 33),
    (['security onions', 'network administrators', 'patches per day'], 33),
    (['automatic alerts', 'network administrators', 'SOC operators'], 33),
    (['security onions', 'network administrators', 'honeypots'], 33),
    (['security onions', 'network administrators', 'SOC operators'], 33),
    (['security onions', 'automatic alerts', 'SOC operators'], 33),
    (['SOC operators', 'honeypots', 'patches per day'], 33),
    (['automatic alerts', 'network administrators', 'deployed decoys'], 33),
    (['network administrators', 'honeypots', 'patches per day'], 33),
     (['security onions', 'honeypots', 'deployed decoys'], 24), # Example: Total impact from x, y, and z must be at least 24
]

for var_names, lower_bound in constraints_vars:
    m.addConstr(sum([impact[var_name] * variables[var_name] for var_name in var_names]) >= lower_bound)

m.addConstr(-1 * variables['automatic alerts'] + 4 * variables['patches per day'] >= 0)
m.addConstr(impact['automatic alerts'] * variables['automatic alerts'] + impact['network administrators'] * variables['network administrators'] + impact['honeypots'] * variables['honeypots'] <= 160)
m.addConstr(impact['honeypots'] * variables['honeypots'] + impact['deployed decoys'] * variables['deployed decoys'] + impact['patches per day'] * variables['patches per day'] <= 50)
m.addConstr(impact['security onions'] * variables['security onions'] + impact['network administrators'] * variables['network administrators'] + impact['patches per day'] * variables['patches per day'] <= 116)
m.addConstr(impact['security onions'] * variables['security onions'] + impact['SOC operators'] * variables['SOC operators'] + impact['deployed decoys'] * variables['deployed decoys'] <= 203)
m.addConstr(impact['automatic alerts'] * variables['automatic alerts'] + impact['SOC operators'] * variables['SOC operators'] + impact['patches per day'] * variables['patches per day'] <= 241)
m.addConstr(impact['automatic alerts'] * variables['automatic alerts'] + impact['deployed decoys'] * variables['deployed decoys'] + impact['patches per day'] * variables['patches per day'] <= 259)
m.addConstr(impact['network administrators'] * variables['network administrators'] + impact['SOC operators'] * variables['SOC operators'] + impact['honeypots'] * variables['honeypots'] <= 88)
m.addConstr(impact['security onions'] * variables['security onions'] + impact['automatic alerts'] * variables['automatic alerts'] + impact['network administrators'] * variables['network administrators'] <= 211)
m.addConstr(impact['security onions'] * variables['security onions'] + impact['SOC operators'] * variables['SOC operators'] + impact['honeypots'] * variables['honeypots'] <= 177)
m.addConstr(impact['automatic alerts'] * variables['automatic alerts'] + impact['honeypots'] * variables['honeypots'] + impact['patches per day'] * variables['patches per day'] <= 201)
m.addConstr(impact['network administrators'] * variables['network administrators'] + impact['SOC operators'] * variables['SOC operators'] + impact['deployed decoys'] * variables['deployed decoys'] <= 80)



# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print("Optimization ended with status:", m.status)

```
