## Step 1: Define the symbolic representation of the variables
The variables are: 
- 'network administrators' 
- 'intrusion analysts' 
- 'Mbps bandwidth allocated to monitoring' 
- 'patches per day' 
- 'SOC operators'

Let's denote them as:
- $x_0$ : 'network administrators'
- $x_1$ : 'intrusion analysts'
- $x_2$ : 'Mbps bandwidth allocated to monitoring'
- $x_3$ : 'patches per day'
- $x_4$ : 'SOC operators'

## Step 2: Formulate the objective function
The objective function to maximize is:
$7.63x_0 + 7.32x_1 + 7.5x_2 + 3.2x_3 + 1.63x_4$

## Step 3: Define the constraints
1. $10x_0 \leq 104$
2. $2x_0 \leq 114$
3. $7x_1 \leq 104$
4. $8x_1 \leq 114$
5. $9x_2 \leq 104$
6. $11x_2 \leq 114$
7. $9x_3 \leq 104$
8. $10x_3 \leq 114$
9. $11x_4 \leq 104$
10. $2x_4 \leq 114$
11. $7x_1 + 11x_4 \geq 14$
12. $8x_1 + 10x_3 \geq 11$
13. $2x_0 + 8x_1 \geq 16$
14. $8x_1 + 2x_4 \geq 9$
15. $11x_2 + 10x_3 \geq 20$
16. $2x_0 + 8x_1 + 11x_2 \geq 20$
17. $8x_1 + 11x_2 + 2x_4 \geq 20$
18. $2x_0 + 10x_3 + 2x_4 \geq 20$
19. $2x_0 + 8x_1 + 11x_2 \geq 11$
20. $8x_1 + 11x_2 + 2x_4 \geq 11$
21. $2x_0 + 10x_3 + 2x_4 \geq 11$
22. $2x_0 + 8x_1 + 11x_2 \geq 12$
23. $8x_1 + 11x_2 + 2x_4 \geq 12$
24. $2x_0 + 10x_3 + 2x_4 \geq 12$
25. $-9x_0 + 9x_1 + 10x_3 \geq 0$
26. $9x_2 + 9x_3 \leq 85$
27. $10x_0 + 9x_3 \leq 92$
28. $7x_1 + 9x_2 + 9x_3 \leq 36$
29. $10x_0 + 7x_1 + 9x_3 \leq 54$
30. $10x_0 + 7x_1 + 9x_2 + 9x_3 + 11x_4 \leq 54$
31. $8x_1 + 10x_3 \leq 69$
32. $2x_0 + 8x_1 \leq 70$
33. $2x_0 + 2x_4 \leq 81$
34. $8x_1 + 11x_2 \leq 39$
35. $2x_0 + 8x_1 + 11x_2 \leq 44$
36. $11x_2 + 10x_3 + 2x_4 \leq 27$
37. $2x_0 + 10x_3 + 2x_4 \leq 108$
38. $2x_0 + 11x_2 + 2x_4 \leq 56$
39. $8x_1 + 11x_2 + 10x_3 \leq 70$
40. $2x_0 + 8x_1 + 11x_2 + 10x_3 + 2x_4 \leq 105$

## 4: Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'network administrators'),
        ('x1', 'intrusion analysts'),
        ('x2', 'Mbps bandwidth allocated to monitoring'),
        ('x3', 'patches per day'),
        ('x4', 'SOC operators')
    ],
    'objective_function': '7.63*x0 + 7.32*x1 + 7.5*x2 + 3.2*x3 + 1.63*x4',
    'constraints': [
        '10*x0 <= 104',
        '2*x0 <= 114',
        '7*x1 <= 104',
        '8*x1 <= 114',
        '9*x2 <= 104',
        '11*x2 <= 114',
        '9*x3 <= 104',
        '10*x3 <= 114',
        '11*x4 <= 104',
        '2*x4 <= 114',
        '7*x1 + 11*x4 >= 14',
        '8*x1 + 10*x3 >= 11',
        '2*x0 + 8*x1 >= 16',
        '8*x1 + 2*x4 >= 9',
        '11*x2 + 10*x3 >= 20',
        '2*x0 + 8*x1 + 11*x2 >= 20',
        '8*x1 + 11*x2 + 2*x4 >= 20',
        '2*x0 + 10*x3 + 2*x4 >= 20',
        '2*x0 + 8*x1 + 11*x2 >= 11',
        '8*x1 + 11*x2 + 2*x4 >= 11',
        '2*x0 + 10*x3 + 2*x4 >= 11',
        '2*x0 + 8*x1 + 11*x2 >= 12',
        '8*x1 + 11*x2 + 2*x4 >= 12',
        '2*x0 + 10*x3 + 2*x4 >= 12',
        '-9*x0 + 9*x1 + 10*x3 >= 0',
        '9*x2 + 9*x3 <= 85',
        '10*x0 + 9*x3 <= 92',
        '7*x1 + 9*x2 + 9*x3 <= 36',
        '10*x0 + 7*x1 + 9*x3 <= 54',
        '10*x0 + 7*x1 + 9*x2 + 9*x3 + 11*x4 <= 54',
        '8*x1 + 10*x3 <= 69',
        '2*x0 + 8*x1 <= 70',
        '2*x0 + 2*x4 <= 81',
        '8*x1 + 11*x2 <= 39',
        '2*x0 + 8*x1 + 11*x2 <= 44',
        '11*x2 + 10*x3 + 2*x4 <= 27',
        '2*x0 + 10*x3 + 2*x4 <= 108',
        '2*x0 + 11*x2 + 2*x4 <= 56',
        '8*x1 + 11*x2 + 10*x3 <= 70',
        '2*x0 + 8*x1 + 11*x2 + 10*x3 + 2*x4 <= 105'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name='network_administrators', vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name='intrusion_analysts', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='mbps_bandwidth_allocated_to_monitoring', vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name='patches_per_day', vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name='soc_operators', vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(7.63 * x0 + 7.32 * x1 + 7.5 * x2 + 3.2 * x3 + 1.63 * x4, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(10 * x0 <= 104)
    model.addConstr(2 * x0 <= 114)
    model.addConstr(7 * x1 <= 104)
    model.addConstr(8 * x1 <= 114)
    model.addConstr(9 * x2 <= 104)
    model.addConstr(11 * x2 <= 114)
    model.addConstr(9 * x3 <= 104)
    model.addConstr(10 * x3 <= 114)
    model.addConstr(11 * x4 <= 104)
    model.addConstr(2 * x4 <= 114)
    model.addConstr(7 * x1 + 11 * x4 >= 14)
    model.addConstr(8 * x1 + 10 * x3 >= 11)
    model.addConstr(2 * x0 + 8 * x1 >= 16)
    model.addConstr(8 * x1 + 2 * x4 >= 9)
    model.addConstr(11 * x2 + 10 * x3 >= 20)
    model.addConstr(2 * x0 + 8 * x1 + 11 * x2 >= 20)
    model.addConstr(8 * x1 + 11 * x2 + 2 * x4 >= 20)
    model.addConstr(2 * x0 + 10 * x3 + 2 * x4 >= 20)
    model.addConstr(2 * x0 + 8 * x1 + 11 * x2 >= 11)
    model.addConstr(8 * x1 + 11 * x2 + 2 * x4 >= 11)
    model.addConstr(2 * x0 + 10 * x3 + 2 * x4 >= 11)
    model.addConstr(2 * x0 + 8 * x1 + 11 * x2 >= 12)
    model.addConstr(8 * x1 + 11 * x2 + 2 * x4 >= 12)
    model.addConstr(2 * x0 + 10 * x3 + 2 * x4 >= 12)
    model.addConstr(-9 * x0 + 9 * x1 + 10 * x3 >= 0)
    model.addConstr(9 * x2 + 9 * x3 <= 85)
    model.addConstr(10 * x0 + 9 * x3 <= 92)
    model.addConstr(7 * x1 + 9 * x2 + 9 * x3 <= 36)
    model.addConstr(10 * x0 + 7 * x1 + 9 * x3 <= 54)
    model.addConstr(10 * x0 + 7 * x1 + 9 * x2 + 9 * x3 + 11 * x4 <= 54)
    model.addConstr(8 * x1 + 10 * x3 <= 69)
    model.addConstr(2 * x0 + 8 * x1 <= 70)
    model.addConstr(2 * x0 + 2 * x4 <= 81)
    model.addConstr(8 * x1 + 11 * x2 <= 39)
    model.addConstr(2 * x0 + 8 * x1 + 11 * x2 <= 44)
    model.addConstr(11 * x2 + 10 * x3 + 2 * x4 <= 27)
    model.addConstr(2 * x0 + 10 * x3 + 2 * x4 <= 108)
    model.addConstr(2 * x0 + 11 * x2 + 2 * x4 <= 56)
    model.addConstr(8 * x1 + 11 * x2 + 10 * x3 <= 70)
    model.addConstr(2 * x0 + 8 * x1 + 11 * x2 + 10 * x3 + 2 * x4 <= 105)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Network Administrators: ", x0.varValue)
        print("Intrusion Analysts: ", x1.varValue)
        print("Mbps Bandwidth Allocated to Monitoring: ", x2.varValue)
        print("Patches per Day: ", x3.varValue)
        print("SOC Operators: ", x4.varValue)
    else:
        print("The model is infeasible.")

solve_optimization_problem()
```