## Step 1: Define the symbolic representation of the problem
The problem involves three variables: honeypots, system administrators, and automatic alerts, which we can denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $8x_0^2 + 6x_0x_1 + 5x_1^2 + 3x_1x_2$.

## 3: List the constraints in symbolic notation
Constraints:
1. $3x_0 + 9x_1 + x_2 \leq 136$
2. $10x_0 + x_1 + 10x_2 \leq 68$
3. $9x_0 + x_1 + 9x_2 \leq 67$
4. $7x_0 + 3x_1 + 7x_2 \leq 47$
5. $10x_0 + 6x_1 + 4x_2 \leq 61$
6. $3x_0 + 9x_1 \geq 31$
7. $9x_1 + x_2 \geq 25$
8. $x_0^2 + x_1^2 + x_2^2 \geq 43$
9. $x_0 + x_1 + x_2 \geq 43$
10. $x_0^2 + x_1^2 \geq 9$
11. $x_1 + x_2 \geq 21$
12. $x_0 + x_1 + x_2 \geq 21$
13. $x_1 + x_2 \geq 16$
14. $x_0 + x_1 \geq 20$
15. $x_0 + x_2 \geq 13$
16. $x_0^2 + x_1^2 + x_2^2 \geq 20$
17. $x_0 + x_1 + x_2 \geq 20$
18. $x_0^2 + x_1^2 \geq 8$
19. $x_0 + x_1 + x_2 \geq 8$
20. $x_1 + x_2 \geq 10$
21. $x_0 + x_2 \geq 16$
22. $x_0 + x_1 \geq 7$
23. $x_0 + x_1 + x_2 \geq 7$
24. $5x_0 - 8x_2 \geq 0$
25. $-2x_0 + 5x_1 \geq 0$
26. $x_1^2 + x_2^2 \leq 108$
27. $x_0^2 + x_2^2 \leq 117$
28. $x_0 + x_1 + x_2 \leq 101$
29. $x_0^2 + x_2^2 \leq 24$
30. $x_0^2 + x_1^2 \leq 66$
31. $x_0 + x_1 \leq 17$
32. $x_1^2 + x_2^2 \leq 35$
33. $x_0^2 + x_1^2 + x_2^2 \leq 34$
34. $x_0 + x_2 \leq 48$

## 4: Define the symbolic variables and constraints for the JSON output
```json
{
    'sym_variables': [
        ('x0', 'honeypots'),
        ('x1', 'system administrators'),
        ('x2', 'automatic alerts')
    ],
    'objective_function': '8*x0^2 + 6*x0*x1 + 5*x1^2 + 3*x1*x2',
    'constraints': [
        '3*x0 + 9*x1 + x2 <= 136',
        '10*x0 + x1 + 10*x2 <= 68',
        '9*x0 + x1 + 9*x2 <= 67',
        '7*x0 + 3*x1 + 7*x2 <= 47',
        '10*x0 + 6*x1 + 4*x2 <= 61',
        '3*x0 + 9*x1 >= 31',
        '9*x1 + x2 >= 25',
        'x0^2 + x1^2 + x2^2 >= 43',
        'x0 + x1 + x2 >= 43',
        'x0^2 + x1^2 >= 9',
        'x1 + x2 >= 21',
        'x0 + x1 + x2 >= 21',
        'x1 + x2 >= 16',
        'x0 + x1 >= 20',
        'x0 + x2 >= 13',
        'x0^2 + x1^2 + x2^2 >= 20',
        'x0 + x1 + x2 >= 20',
        'x0^2 + x1^2 >= 8',
        'x0 + x1 + x2 >= 8',
        'x1 + x2 >= 10',
        'x0 + x2 >= 16',
        'x0 + x1 >= 7',
        'x0 + x1 + x2 >= 7',
        '5*x0 - 8*x2 >= 0',
        '-2*x0 + 5*x1 >= 0',
        'x1^2 + x2^2 <= 108',
        'x0^2 + x2^2 <= 117',
        'x0 + x1 + x2 <= 101',
        'x0^2 + x2^2 <= 24',
        'x0^2 + x1^2 <= 66',
        'x0 + x1 <= 17',
        'x1^2 + x2^2 <= 35',
        'x0^2 + x1^2 + x2^2 <= 34',
        'x0 + x2 <= 48'
    ]
}
```

## 5: Write the Gurobi code
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="honeypots", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="system_administrators", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="automatic_alerts", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(8 * x0**2 + 6 * x0 * x1 + 5 * x1**2 + 3 * x1 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(3 * x0 + 9 * x1 + x2 <= 136)
    model.addConstr(10 * x0 + x1 + 10 * x2 <= 68)
    model.addConstr(9 * x0 + x1 + 9 * x2 <= 67)
    model.addConstr(7 * x0 + 3 * x1 + 7 * x2 <= 47)
    model.addConstr(10 * x0 + 6 * x1 + 4 * x2 <= 61)
    model.addConstr(3 * x0 + 9 * x1 >= 31)
    model.addConstr(9 * x1 + x2 >= 25)
    model.addConstr(x0**2 + x1**2 + x2**2 >= 43)
    model.addConstr(x0 + x1 + x2 >= 43)
    model.addConstr(x0**2 + x1**2 >= 9)
    model.addConstr(x1 + x2 >= 21)
    model.addConstr(x0 + x1 + x2 >= 21)
    model.addConstr(x1 + x2 >= 16)
    model.addConstr(x0 + x1 >= 20)
    model.addConstr(x0 + x2 >= 13)
    model.addConstr(x0**2 + x1**2 + x2**2 >= 20)
    model.addConstr(x0 + x1 + x2 >= 20)
    model.addConstr(x0**2 + x1**2 >= 8)
    model.addConstr(x0 + x1 + x2 >= 8)
    model.addConstr(x1 + x2 >= 10)
    model.addConstr(x0 + x2 >= 16)
    model.addConstr(x0 + x1 >= 7)
    model.addConstr(x0 + x1 + x2 >= 7)
    model.addConstr(5 * x0 - 8 * x2 >= 0)
    model.addConstr(-2 * x0 + 5 * x1 >= 0)
    model.addConstr(x1**2 + x2**2 <= 108)
    model.addConstr(x0**2 + x2**2 <= 117)
    model.addConstr(x0 + x1 + x2 <= 101)
    model.addConstr(x0**2 + x2**2 <= 24)
    model.addConstr(x0**2 + x1**2 <= 66)
    model.addConstr(x0 + x1 <= 17)
    model.addConstr(x1**2 + x2**2 <= 35)
    model.addConstr(x0**2 + x1**2 + x2**2 <= 34)
    model.addConstr(x0 + x2 <= 48)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Honeypots: ", x0.varValue)
        print("System Administrators: ", x1.varValue)
        print("Automatic Alerts: ", x2.varValue)
    else:
        print("No optimal solution found")

optimize_problem()
```