## Step 1: Define the variables and their corresponding symbolic representation
Let's denote the variables as follows:
- $x_0$ : network administrators
- $x_1$ : honeypots
- $x_2$ : automatic alerts
- $x_3$ : pen testers
- $x_4$ : intrusion analysts
- $x_5$ : SOC operators

## Step 2: Formulate the objective function
The objective function to maximize is: $8x_0 + 9x_1 + 4x_2 + 9x_3 + 9x_4 + 6x_5$

## 3: List all the constraints
1. $3x_0 + 2x_1 + 5x_2 + x_3 + x_4 + 7x_5 \leq 135$ (dollar cost constraint)
2. $6x_0 + 5x_1 + 6x_2 + 4x_3 + 2x_4 + 2x_5 \leq 137$ (power consumption constraint)
3. $3x_0 + x_3 \geq 12$ (minimum spend on network administrators and pen testers)
4. $5x_2 + 7x_5 \geq 7$ (minimum spend on automatic alerts and SOC operators)
5. $2x_1 + x_4 + 7x_5 \geq 14$ (minimum spend on honeypots, intrusion analysts, and SOC operators)
6. $6x_0 + 6x_2 + 2x_4 \geq 17$ (minimum power consumption from network administrators, automatic alerts, and intrusion analysts)
7. $6x_2 + 4x_3 + 2x_4 \geq 17$ (power consumption from automatic alerts, pen testers, and intrusion analysts)
8. $6x_0 + 5x_1 + 2x_5 \geq 17$ (power consumption from network administrators, honeypots, and SOC operators)
9. $6x_0 + 6x_2 + 4x_3 \geq 17$ (power consumption from network administrators, automatic alerts, and pen testers)
10. $6x_0 + 6x_2 + 2x_4 \geq 19$ 
11. $6x_2 + 4x_3 + 2x_4 \geq 19$ 
12. $6x_0 + 5x_1 + 2x_5 \geq 19$ 
13. $6x_0 + 6x_2 + 4x_3 \geq 22$ 
14. $6x_0 + 6x_2 + 2x_4 \geq 22$ 
15. $6x_2 + 4x_3 + 2x_4 \geq 22$ 
16. $6x_0 + 5x_1 + 2x_5 \geq 22$ 
17. $2x_1 + 5x_2 \leq 96$ (cost constraint on honeypots and automatic alerts)
18. $3x_0 + 7x_5 \leq 59$ (cost constraint on network administrators and SOC operators)
19. $3x_0 + 2x_1 \leq 135$ (cost constraint on network administrators and honeypots)
20. $x_3 + 7x_5 \leq 94$ (cost constraint on pen testers and SOC operators)
21. $5x_2 + x_3 \leq 38$ (cost constraint on automatic alerts and pen testers)
22. $5x_2 + x_3 + 7x_5 \leq 118$ 
23. $3x_0 + 5x_2 + x_3 \leq 115$ 
24. $3x_0 + 2x_1 + 5x_2 + x_3 + x_4 + 7x_5 \leq 115$ 
25. $6x_2 + 2x_4 \leq 82$ (power constraint on automatic alerts and intrusion analysts)
26. $6x_2 + 2x_5 \leq 82$ 
27. $5x_1 + 6x_2 \leq 87$ 
28. $2x_4 + 2x_5 \leq 65$ 
29. $6x_0 + 4x_3 \leq 82$ 
30. $6x_0 + 6x_2 + 2x_4 \leq 81$ 
31. $6x_0 + 6x_2 + 4x_3 \leq 77$ 
32. $6x_2 + 4x_3 + 2x_5 \leq 66$ 
33. $6x_0 + 5x_1 + 4x_3 \leq 38$ 
34. $6x_0 + 5x_1 + 6x_2 \leq 45$ 
35. $5x_1 + 6x_2 + 2x_5 \leq 65$ 
36. $6x_0 + 2x_4 + 2x_5 \leq 124$ 
37. $6x_0 + 5x_1 + 2x_4 \leq 109$ 
38. $5x_1 + 6x_2 + 4x_3 \leq 109$ 
39. $5x_1 + 4x_3 + 2x_5 \leq 99$ 
40. $6x_0 + 5x_1 + 2x_5 \leq 68$ 
41. $6x_2 + 2x_4 + 2x_5 \leq 106$ 
42. $6x_0 + 6x_2 + 2x_5 \leq 29$ 
43. $6x_0 + 4x_3 + 2x_4 \leq 126$ 
44. $5x_1 + 6x_2 + 2x_4 \leq 123$ 
45. $6x_0 + 5x_1 + 6x_2 + 4x_3 + 2x_4 + 2x_5 \leq 123$

## 4: Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'network administrators'),
        ('x1', 'honeypots'),
        ('x2', 'automatic alerts'),
        ('x3', 'pen testers'),
        ('x4', 'intrusion analysts'),
        ('x5', 'SOC operators')
    ],
    'objective_function': '8*x0 + 9*x1 + 4*x2 + 9*x3 + 9*x4 + 6*x5',
    'constraints': [
        '3*x0 + 2*x1 + 5*x2 + x3 + x4 + 7*x5 <= 135',
        '6*x0 + 5*x1 + 6*x2 + 4*x3 + 2*x4 + 2*x5 <= 137',
        '3*x0 + x3 >= 12',
        '5*x2 + 7*x5 >= 7',
        '2*x1 + x4 + 7*x5 >= 14',
        '6*x0 + 6*x2 + 2*x4 >= 17',
        '6*x2 + 4*x3 + 2*x4 >= 17',
        '6*x0 + 5*x1 + 2*x5 >= 17',
        '6*x0 + 6*x2 + 4*x3 >= 17',
        '6*x0 + 6*x2 + 2*x4 >= 19',
        '6*x2 + 4*x3 + 2*x4 >= 19',
        '6*x0 + 5*x1 + 2*x5 >= 19',
        '6*x0 + 6*x2 + 4*x3 >= 22',
        '6*x0 + 6*x2 + 2*x4 >= 22',
        '6*x2 + 4*x3 + 2*x4 >= 22',
        '6*x0 + 5*x1 + 2*x5 >= 22',
        '2*x1 + 5*x2 <= 96',
        '3*x0 + 7*x5 <= 59',
        '3*x0 + 2*x1 <= 135',
        'x3 + 7*x5 <= 94',
        '5*x2 + x3 <= 38',
        '5*x2 + x3 + 7*x5 <= 118',
        '3*x0 + 5*x2 + x3 <= 115',
        '3*x0 + 2*x1 + 5*x2 + x3 + x4 + 7*x5 <= 115',
        '6*x2 + 2*x4 <= 82',
        '6*x2 + 2*x5 <= 82',
        '5*x1 + 6*x2 <= 87',
        '2*x4 + 2*x5 <= 65',
        '6*x0 + 4*x3 <= 82',
        '6*x0 + 6*x2 + 2*x4 <= 81',
        '6*x0 + 6*x2 + 4*x3 <= 77',
        '6*x2 + 4*x3 + 2*x5 <= 66',
        '6*x0 + 5*x1 + 4*x3 <= 38',
        '6*x0 + 5*x1 + 6*x2 <= 45',
        '5*x1 + 6*x2 + 2*x5 <= 65',
        '6*x0 + 2*x4 + 2*x5 <= 124',
        '6*x0 + 5*x1 + 2*x4 <= 109',
        '5*x1 + 6*x2 + 4*x3 <= 109',
        '5*x1 + 4*x3 + 2*x5 <= 99',
        '6*x0 + 5*x1 + 2*x5 <= 68',
        '6*x2 + 2*x4 + 2*x5 <= 106',
        '6*x0 + 6*x2 + 2*x5 <= 29',
        '6*x0 + 4*x3 + 2*x4 <= 126',
        '5*x1 + 6*x2 + 2*x4 <= 123',
        '6*x0 + 5*x1 + 6*x2 + 4*x3 + 2*x4 + 2*x5 <= 123'
    ]
}
```

## 5: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="network_administrators", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="honeypots", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="automatic_alerts", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="pen_testers", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="intrusion_analysts", vtype=gurobi.GRB.INTEGER)
    x5 = model.addVar(name="SOC_operators", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(8*x0 + 9*x1 + 4*x2 + 9*x3 + 9*x4 + 6*x5, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(3*x0 + 2*x1 + 5*x2 + x3 + x4 + 7*x5 <= 135)
    model.addConstr(6*x0 + 5*x1 + 6*x2 + 4*x3 + 2*x4 + 2*x5 <= 137)
    model.addConstr(3*x0 + x3 >= 12)
    model.addConstr(5*x2 + 7*x5 >= 7)
    model.addConstr(2*x1 + x4 + 7*x5 >= 14)
    model.addConstr(6*x0 + 6*x2 + 2*x4 >= 17)
    model.addConstr(6*x2 + 4*x3 + 2*x4 >= 17)
    model.addConstr(6*x0 + 5*x1 + 2*x5 >= 17)
    model.addConstr(6*x0 + 6*x2 + 4*x3 >= 17)
    model.addConstr(6*x0 + 6*x2 + 2*x4 >= 19)
    model.addConstr(6*x2 + 4*x3 + 2*x4 >= 19)
    model.addConstr(6*x0 + 5*x1 + 2*x5 >= 19)
    model.addConstr(6*x0 + 6*x2 + 4*x3 >= 22)
    model.addConstr(6*x0 + 6*x2 + 2*x4 >= 22)
    model.addConstr(6*x2 + 4*x3 + 2*x4 >= 22)
    model.addConstr(6*x0 + 5*x1 + 2*x5 >= 22)
    model.addConstr(2*x1 + 5*x2 <= 96)
    model.addConstr(3*x0 + 7*x5 <= 59)
    model.addConstr(3*x0 + 2*x1 <= 135)
    model.addConstr(x3 + 7*x5 <= 94)
    model.addConstr(5*x2 + x3 <= 38)
    model.addConstr(5*x2 + x3 + 7*x5 <= 118)
    model.addConstr(3*x0 + 5*x2 + x3 <= 115)
    model.addConstr(3*x0 + 2*x1 + 5*x2 + x3 + x4 + 7*x5 <= 115)
    model.addConstr(6*x2 + 2*x4 <= 82)
    model.addConstr(6*x2 + 2*x5 <= 82)
    model.addConstr(5*x1 + 6*x2 <= 87)
    model.addConstr(2*x4 + 2*x5 <= 65)
    model.addConstr(6*x0 + 4*x3 <= 82)
    model.addConstr(6*x0 + 6*x2 + 2*x4 <= 81)
    model.addConstr(6*x0 + 6*x2 + 4*x3 <= 77)
    model.addConstr(6*x2 + 4*x3 + 2*x5 <= 66)
    model.addConstr(6*x0 + 5*x1 + 4*x3 <= 38)
    model.addConstr(6*x0 + 5*x1 + 6*x2 <= 45)
    model.addConstr(5*x1 + 6*x2 + 2*x5 <= 65)
    model.addConstr(6*x0 + 2*x4 + 2*x5 <= 124)
    model.addConstr(6*x0 + 5*x1 + 2*x4 <= 109)
    model.addConstr(5*x1 + 6*x2 + 4*x3 <= 109)
    model.addConstr(5*x1 + 4*x3 + 2*x5 <= 99)
    model.addConstr(6*x0 + 5*x1 + 2*x5 <= 68)
    model.addConstr(6*x2 + 2*x4 + 2*x5 <= 106)
    model.addConstr(6*x0 + 6*x2 + 2*x5 <= 29)
    model.addConstr(6*x0 + 4*x3 + 2*x4 <= 126)
    model.addConstr(5*x1 + 6*x2 + 2*x4 <= 123)
    model.addConstr(6*x0 + 5*x1 + 6*x2 + 4*x3 + 2*x4 + 2*x5 <= 123)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("network administrators: ", x0.varValue)
        print("honeypots: ", x1.varValue)
        print("automatic alerts: ", x2.varValue)
        print("pen testers: ", x3.varValue)
        print("intrusion analysts: ", x4.varValue)
        print("SOC operators: ", x5.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```