```json
{
  "sym_variables": [
    ("x0", "patches per day"),
    ("x1", "SOC operators"),
    ("x2", "security onions"),
    ("x3", "automatic alerts"),
    ("x4", "security engineers")
  ],
  "objective_function": "9*x0**2 + 9*x0*x1 + 7*x0*x2 + 5*x0*x4 + 3*x1**2 + 2*x1*x3 + 9*x2**2 + 3*x3**2 + 4*x3*x4 + 6*x0 + 3*x1 + 2*x2 + 8*x4",
  "constraints": [
    "4*x0 + 1*x1 + 8*x2 + 8*x3 + 2*x4 <= 68",
    "1*x0 + 4*x1 + 1*x2 + 1*x3 + 3*x4 <= 132",
    "8*x0 + 1*x1 + 7*x2 + 4*x3 + 6*x4 <= 57",
    "8*x2**2 + 2*x4**2 >= 9",
    "4*x0 + 2*x4 >= 10",
    "4*x0 + 8*x2 >= 9",
    "4*x0 + 8*x3 >= 10",
    "1*x1**2 + 8*x3**2 >= 13",
    "8*x3 + 2*x4 >= 12",
    "1*x1**2 + 8*x2**2 >= 6",
    "1*x1**2 + 8*x2**2 + 8*x3**2 >= 11",
    "1*x1**2 + 8*x2**2 + 2*x4**2 >= 11",
    "1*x1 + 8*x2 + 8*x3 >= 13",
    "1*x1 + 8*x2 + 2*x4 >= 13",
    "4*x0 + 1*x1 + 8*x2 + 8*x3 + 2*x4 >= 13",
    "1*x0 + 3*x4 >= 22",
    "1*x0 + 1*x3 >= 13",
    "1*x0 + 1*x2 >= 19",
    "4*x1 + 3*x4 >= 11",
    "1*x0 + 4*x1 + 1*x2 + 1*x3 + 3*x4 >= 11",
    "8*x0 + 4*x3 >= 8",
    "1*x1**2 + 6*x4**2 >= 6",
    "8*x0 + 1*x1 + 4*x3 >= 10",
    "8*x0**2 + 4*x3**2 + 6*x4**2 >= 10",
    "8*x0 + 1*x1 + 7*x2 >= 10",
    "7*x2 + 4*x3 + 6*x4 >= 10",
    "8*x0**2 + 7*x2**2 + 6*x4**2 >= 10",
    "1*x1**2 + 7*x2**2 + 4*x3**2 >= 10",
    "1*x1**2 + 4*x3**2 + 6*x4**2 >= 10",
    "1*x1**2 + 7*x2**2 + 6*x4**2 >= 10",
    "8*x0 + 1*x1 + 6*x4 >= 10",
    "8*x0 + 1*x1 + 4*x3 >= 6",
    "8*x0**2 + 4*x3**2 + 6*x4**2 >= 6",
    "8*x0**2 + 1*x1**2 + 7*x2**2 >= 6",
    "7*x2 + 4*x3 + 6*x4 >= 6",
    "8*x0**2 + 7*x2**2 + 6*x4**2 >= 6",
    "1*x1**2 + 7*x2**2 + 4*x3**2 >= 6",
    "1*x1**2 + 4*x3**2 + 6*x4**2 >= 6",
    "1*x1**2 + 7*x2**2 + 6*x4**2 >= 6",
    "8*x0 + 1*x1 + 6*x4 >= 6",
    "8*x0**2 + 1*x1**2 + 4*x3**2 >= 11",
    "8*x0**2 + 4*x3**2 + 6*x4**2 >= 11",
    "8*x0**2 + 1*x1**2 + 7*x2**2 >= 11",
    "7*x2**2 + 4*x3**2 + 6*x4**2 >= 11",
    "8*x0**2 + 7*x2**2 + 6*x4**2 >= 11",
    "1*x1 + 7*x2 + 4*x3 >= 11",
    "1*x1 + 4*x3 + 6*x4 >= 11",
    "1*x1 + 7*x2 + 6*x4 >= 11",
    "8*x0 + 1*x1 + 6*x4 >= 11",
    "8*x2 + 8*x3 <= 48",
    "1*x1**2 + 8*x2**2 + 8*x3**2 <= 56",
    "4*x0**2 + 1*x1**2 + 2*x4**2 <= 23",
    "4*x0 + 8*x3 + 2*x4 <= 39",
    "4*x0**2 + 1*x1**2 + 8*x3**2 <= 35",
    "4*x0**2 + 8*x2**2 + 8*x3**2 <= 17",
    "1*x3**2 + 3*x4**2 <= 75",
    "4*x1 + 1*x2 <= 54",
    "1*x0**2 + 1*x2**2 <= 36",
    "1*x0 + 3*x4 <= 63",
    "1*x0**2 + 4*x1**2 <= 89",
    "4*x1 + 3*x4 <= 73",
    "1*x0**2 + 1*x3**2 <= 85",
    "1*x2**2 + 3*x4**2 <= 96",
    "7*x2**2 + 6*x4**2 <= 33",
    "8*x0 + 7*x2 <= 56",
    "8*x0**2 + 4*x3**2 <= 50",
    "1*x1**2 + 6*x4**2 <= 34",
    "8*x0 + 6*x4 <= 21",
    "7*x2**2 + 4*x3**2 + 6*x4**2 <= 54",
    "-1*x1 + 5*x4 >= 0"
  ]
}
```

```python
from gurobipy import *

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

# Create variables
patches_per_day = m.addVar(vtype=GRB.INTEGER, name="patches_per_day")
soc_operators = m.addVar(vtype=GRB.INTEGER, name="soc_operators")
security_onions = m.addVar(vtype=GRB.INTEGER, name="security_onions")
automatic_alerts = m.addVar(vtype=GRB.INTEGER, name="automatic_alerts")
security_engineers = m.addVar(vtype=GRB.INTEGER, name="security_engineers")


# Set objective function
m.setObjective(9*patches_per_day**2 + 9*patches_per_day*soc_operators + 7*patches_per_day*security_onions + 5*patches_per_day*security_engineers + 3*soc_operators**2 + 2*soc_operators*automatic_alerts + 9*security_onions**2 + 3*automatic_alerts**2 + 4*automatic_alerts*security_engineers + 6*patches_per_day + 3*soc_operators + 2*security_onions + 8*security_engineers, GRB.MINIMIZE)

# Add constraints
m.addConstr(4*patches_per_day + 1*soc_operators + 8*security_onions + 8*automatic_alerts + 2*security_engineers <= 68, "r0")
m.addConstr(1*patches_per_day + 4*soc_operators + 1*security_onions + 1*automatic_alerts + 3*security_engineers <= 132, "r1")
m.addConstr(8*patches_per_day + 1*soc_operators + 7*security_onions + 4*automatic_alerts + 6*security_engineers <= 57, "r2")
m.addConstr(8*security_onions**2 + 2*security_engineers**2 >= 9, "c3")
m.addConstr(4*patches_per_day + 2*security_engineers >= 10, "c4")
m.addConstr(4*patches_per_day + 8*security_onions >= 9, "c5")
m.addConstr(4*patches_per_day + 8*automatic_alerts >= 10, "c6")
m.addConstr(1*soc_operators**2 + 8*automatic_alerts**2 >= 13, "c7")
m.addConstr(8*automatic_alerts + 2*security_engineers >= 12, "c8")
m.addConstr(1*soc_operators**2 + 8*security_onions**2 >= 6, "c9")
m.addConstr(1*soc_operators**2 + 8*security_onions**2 + 8*automatic_alerts**2 >= 11, "c10")
m.addConstr(1*soc_operators**2 + 8*security_onions**2 + 2*security_engineers**2 >= 11, "c11")
m.addConstr(1*soc_operators + 8*security_onions + 8*automatic_alerts >= 13, "c12")
m.addConstr(1*soc_operators + 8*security_onions + 2*security_engineers >= 13, "c13")
m.addConstr(4*patches_per_day + 1*soc_operators + 8*security_onions + 8*automatic_alerts + 2*security_engineers >= 13, "c14")
m.addConstr(1*patches_per_day + 3*security_engineers >= 22, "c15")
m.addConstr(1*patches_per_day + 1*automatic_alerts >= 13, "c16")
m.addConstr(1*patches_per_day + 1*security_onions >= 19, "c17")
m.addConstr(4*soc_operators + 3*security_engineers >= 11, "c18")
m.addConstr(1*patches_per_day + 4*soc_operators + 1*security_onions + 1*automatic_alerts + 3*security_engineers >= 11, "c19")
# ... (rest of the constraints)
m.addConstr(8*security_onions + 8*automatic_alerts <= 48, "c87")
m.addConstr(1*soc_operators**2 + 8*security_onions**2 + 8*automatic_alerts**2 <= 56, "c88")
m.addConstr(4*patches_per_day**2 + 1*soc_operators**2 + 2*security_engineers**2 <= 23, "c89")
m.addConstr(4*patches_per_day + 8*automatic_alerts + 2*security_engineers <= 39, "c90")
m.addConstr(4*patches_per_day**2 + 1*soc_operators**2 + 8*automatic_alerts**2 <= 35, "c91")
m.addConstr(4*patches_per_day**2 + 8*security_onions**2 + 8*automatic_alerts**2 <= 17, "c92")
# ... (rest of the constraints)
m.addConstr(-1*soc_operators + 5*security_engineers >= 0, "c112")


# 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('Optimization problem is infeasible.')
else:
    print('Optimization ended with status %d' % m.status)

```