## Step 1: Define the symbolic representation of the variables
The variables are ['patches per day', 'system administrators', 'pen testers', 'Mbps bandwidth allocated to monitoring', 'honeypots']. Let's denote them as $x_1, x_2, x_3, x_4, x_5$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $6.19x_1 + 8.45x_2 + 7.49x_3 + 5.66x_4 + 9.2x_5$.

## Step 3: List the constraints in symbolic notation
1. $16x_1 + 12x_2 + 17x_3 + 19x_4 + 32x_5 \leq 783$ (power consumption)
2. $2x_1 + 16x_2 + 20x_3 + 33x_4 + 21x_5 \leq 462$ (data accessibility impact)
3. $12x_2 + 17x_3 + 32x_5 \geq 150$ (power consumption of system administrators, pen testers, and honeypots)
4. $16x_1 + 17x_3 + 32x_5 \geq 150$ (minimum power consumption from patches per day, pen testers, and honeypots)
5. $16x_1 + 12x_2 + 17x_3 \geq 150$ (minimum power consumption from patches per day, system administrators, and pen testers)
6. $16x_1 + 12x_2 + 19x_4 \geq 150$ (patches per day, system administrators, and Mbps bandwidth allocated to monitoring)
7. $12x_2 + 17x_3 + 32x_5 \geq 87$ 
8. $16x_1 + 17x_3 + 32x_5 \geq 87$ 
9. $16x_1 + 12x_2 + 17x_3 \geq 87$ 
10. $16x_1 + 12x_2 + 19x_4 \geq 87$ 
11. $12x_2 + 17x_3 + 32x_5 \geq 114$ 
12. $16x_1 + 17x_3 + 32x_5 \geq 114$ 
13. $16x_1 + 12x_2 + 17x_3 \geq 114$ 
14. $16x_1 + 12x_2 + 19x_4 \geq 114$ 
15. $12x_2 + 32x_5 \leq 561$ (power consumption of system administrators and honeypots)
16. $17x_3 + 32x_5 \leq 257$ (power consumption of pen testers and honeypots)
17. $16x_1 + 19x_4 \leq 760$ (power consumption of patches per day and Mbps bandwidth allocated to monitoring)
18. $19x_4 + 32x_5 \leq 306$ (power consumption of Mbps bandwidth allocated to monitoring and honeypots)
19. $12x_2 + 17x_3 + 19x_4 \leq 679$ 
20. $16x_1 + 19x_4 + 32x_5 \leq 323$ 
21. $16x_1 + 12x_2 + 17x_3 + 19x_4 + 32x_5 \leq 323$ 
22. $33x_4 + 21x_5 \leq 449$ (data accessibility impact of Mbps bandwidth allocated to monitoring and honeypots)
23. $16x_2 + 33x_4 \leq 459$ 
24. $20x_3 + 33x_4 \leq 285$ 
25. $16x_2 + 20x_3 + 33x_4 \leq 377$ 
26. $2x_1 + 16x_2 + 33x_4 \leq 297$ 
27. $16x_2 + 33x_4 + 21x_5 \leq 337$ 
28. $2x_1 + 16x_2 + 21x_5 \leq 285$ 
29. $2x_1 + 16x_2 + 20x_3 + 33x_4 + 21x_5 \leq 285$

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'patches per day'),
        ('x2', 'system administrators'),
        ('x3', 'pen testers'),
        ('x4', 'Mbps bandwidth allocated to monitoring'),
        ('x5', 'honeypots')
    ],
    'objective_function': '6.19*x1 + 8.45*x2 + 7.49*x3 + 5.66*x4 + 9.2*x5',
    'constraints': [
        '16*x1 + 12*x2 + 17*x3 + 19*x4 + 32*x5 <= 783',
        '2*x1 + 16*x2 + 20*x3 + 33*x4 + 21*x5 <= 462',
        '12*x2 + 17*x3 + 32*x5 >= 150',
        '16*x1 + 17*x3 + 32*x5 >= 150',
        '16*x1 + 12*x2 + 17*x3 >= 150',
        '16*x1 + 12*x2 + 19*x4 >= 150',
        '12*x2 + 17*x3 + 32*x5 >= 87',
        '16*x1 + 17*x3 + 32*x5 >= 87',
        '16*x1 + 12*x2 + 17*x3 >= 87',
        '16*x1 + 12*x2 + 19*x4 >= 87',
        '12*x2 + 17*x3 + 32*x5 >= 114',
        '16*x1 + 17*x3 + 32*x5 >= 114',
        '16*x1 + 12*x2 + 17*x3 >= 114',
        '16*x1 + 12*x2 + 19*x4 >= 114',
        '12*x2 + 32*x5 <= 561',
        '17*x3 + 32*x5 <= 257',
        '16*x1 + 19*x4 <= 760',
        '19*x4 + 32*x5 <= 306',
        '12*x2 + 17*x3 + 19*x4 <= 679',
        '16*x1 + 19*x4 + 32*x5 <= 323',
        '16*x1 + 12*x2 + 17*x3 + 19*x4 + 32*x5 <= 323',
        '33*x4 + 21*x5 <= 449',
        '16*x2 + 33*x4 <= 459',
        '20*x3 + 33*x4 <= 285',
        '16*x2 + 20*x3 + 33*x4 <= 377',
        '2*x1 + 16*x2 + 33*x4 <= 297',
        '16*x2 + 33*x4 + 21*x5 <= 337',
        '2*x1 + 16*x2 + 21*x5 <= 285',
        '2*x1 + 16*x2 + 20*x3 + 33*x4 + 21*x5 <= 285'
    ]
}
```

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

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

    # Define variables
    x1 = model.addVar(name="patches_per_day", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="system_administrators", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="pen_testers", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="mbps_bandwidth_allocated_to_monitoring", vtype=gurobi.GRB.INTEGER)
    x5 = model.addVar(name="honeypots", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(6.19*x1 + 8.45*x2 + 7.49*x3 + 5.66*x4 + 9.2*x5, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(16*x1 + 12*x2 + 17*x3 + 19*x4 + 32*x5 <= 783)
    model.addConstr(2*x1 + 16*x2 + 20*x3 + 33*x4 + 21*x5 <= 462)
    model.addConstr(12*x2 + 17*x3 + 32*x5 >= 150)
    model.addConstr(16*x1 + 17*x3 + 32*x5 >= 150)
    model.addConstr(16*x1 + 12*x2 + 17*x3 >= 150)
    model.addConstr(16*x1 + 12*x2 + 19*x4 >= 150)
    model.addConstr(12*x2 + 17*x3 + 32*x5 >= 87)
    model.addConstr(16*x1 + 17*x3 + 32*x5 >= 87)
    model.addConstr(16*x1 + 12*x2 + 17*x3 >= 87)
    model.addConstr(16*x1 + 12*x2 + 19*x4 >= 87)
    model.addConstr(12*x2 + 17*x3 + 32*x5 >= 114)
    model.addConstr(16*x1 + 17*x3 + 32*x5 >= 114)
    model.addConstr(16*x1 + 12*x2 + 17*x3 >= 114)
    model.addConstr(16*x1 + 12*x2 + 19*x4 >= 114)
    model.addConstr(12*x2 + 32*x5 <= 561)
    model.addConstr(17*x3 + 32*x5 <= 257)
    model.addConstr(16*x1 + 19*x4 <= 760)
    model.addConstr(19*x4 + 32*x5 <= 306)
    model.addConstr(12*x2 + 17*x3 + 19*x4 <= 679)
    model.addConstr(16*x1 + 19*x4 + 32*x5 <= 323)
    model.addConstr(16*x1 + 12*x2 + 17*x3 + 19*x4 + 32*x5 <= 323)
    model.addConstr(33*x4 + 21*x5 <= 449)
    model.addConstr(16*x2 + 33*x4 <= 459)
    model.addConstr(20*x3 + 33*x4 <= 285)
    model.addConstr(16*x2 + 20*x3 + 33*x4 <= 377)
    model.addConstr(2*x1 + 16*x2 + 33*x4 <= 297)
    model.addConstr(16*x2 + 33*x4 + 21*x5 <= 337)
    model.addConstr(2*x1 + 16*x2 + 21*x5 <= 285)
    model.addConstr(2*x1 + 16*x2 + 20*x3 + 33*x4 + 21*x5 <= 285)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("patches per day: ", x1.varValue)
        print("system administrators: ", x2.varValue)
        print("pen testers: ", x3.varValue)
        print("Mbps bandwidth allocated to monitoring: ", x4.varValue)
        print("honeypots: ", x5.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```