## Step 1: Define the symbolic representation of the problem
The problem involves maximizing the objective function: $1 \times \text{SOC operators} + 6 \times \text{automatic alerts} + 8 \times \text{system administrators}$. Let's denote SOC operators as $x_0$, automatic alerts as $x_1$, and system administrators as $x_2$.

## 2: Translate the problem into a symbolic optimization problem
The objective function can be written as: $1x_0 + 6x_1 + 8x_2$.

## 3: List all constraints in symbolic notation
Constraints:
1. $15x_0 + 24x_1 + 21x_2 \leq 132$
2. $21x_0 + 22x_1 + 7x_2 \leq 198$
3. $16x_0 + 8x_1 + 2x_2 \leq 128$
4. $16x_0 + 24x_1 + 24x_2 \leq 155$
5. $21x_0 + 24x_1 + 9x_2 \leq 92$
6. $15x_0 + 21x_2 \geq 27$
7. $24x_1 + 21x_2 \geq 37$
8. $15x_0 + 24x_1 + 21x_2 \geq 22$
9. $16x_0 + 24x_1 \geq 37$
10. $24x_1 + 24x_2 \geq 22$
11. $16x_0 + 24x_1 + 24x_2 \geq 44$
12. $21x_0 + 24x_1 + 9x_2 \geq 23$
13. $15x_0 + 24x_1 + 21x_2 \leq 110$
14. $15x_0 + 21x_2 \leq 59$
15. $24x_1 + 21x_2 \leq 110$
16. $21x_0 + 22x_1 + 7x_2 \leq 197$
17. $21x_0 + 22x_1 \leq 190$
18. $21x_0 + 22x_1 + 7x_2 \leq 66$
19. $16x_0 + 24x_1 + 24x_2 \leq 147$
20. $24x_1 + 24x_2 \leq 140$
21. $16x_0 + 24x_1 \leq 53$
22. $16x_0 + 24x_1 + 24x_2 \leq 53$
23. $21x_0 + 9x_2 \leq 81$
24. $21x_0 + 24x_1 \leq 69$
25. $21x_0 + 24x_1 + 9x_2 \leq 69$

## 4: Define the symbolic variables and constraints for output
```json
{
    'sym_variables': [
        ('x0', 'SOC operators'), 
        ('x1', 'automatic alerts'), 
        ('x2', 'system administrators')
    ], 
    'objective_function': '1*x0 + 6*x1 + 8*x2', 
    'constraints': [
        '15*x0 + 24*x1 + 21*x2 <= 132',
        '21*x0 + 22*x1 + 7*x2 <= 198',
        '16*x0 + 8*x1 + 2*x2 <= 128',
        '16*x0 + 24*x1 + 24*x2 <= 155',
        '21*x0 + 24*x1 + 9*x2 <= 92',
        '15*x0 + 21*x2 >= 27',
        '24*x1 + 21*x2 >= 37',
        '15*x0 + 24*x1 + 21*x2 >= 22',
        '16*x0 + 24*x1 >= 37',
        '24*x1 + 24*x2 >= 22',
        '16*x0 + 24*x1 + 24*x2 >= 44',
        '21*x0 + 24*x1 + 9*x2 >= 23',
        '15*x0 + 24*x1 + 21*x2 <= 110',
        '15*x0 + 21*x2 <= 59',
        '24*x1 + 21*x2 <= 110',
        '21*x0 + 22*x1 + 7*x2 <= 197',
        '21*x0 + 22*x1 <= 190',
        '21*x0 + 22*x1 + 7*x2 <= 66',
        '16*x0 + 24*x1 + 24*x2 <= 147',
        '24*x1 + 24*x2 <= 140',
        '16*x0 + 24*x1 <= 53',
        '16*x0 + 24*x1 + 24*x2 <= 53',
        '21*x0 + 9*x2 <= 81',
        '21*x0 + 24*x1 <= 69',
        '21*x0 + 24*x1 + 9*x2 <= 69'
    ]
}
```

## 5: Write the Gurobi code for the optimization problem
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="SOC_operators", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="automatic_alerts", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="system_administrators", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(1*x0 + 6*x1 + 8*x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x0 + 24*x1 + 21*x2 <= 132)
m.addConstr(21*x0 + 22*x1 + 7*x2 <= 198)
m.addConstr(16*x0 + 8*x1 + 2*x2 <= 128)
m.addConstr(16*x0 + 24*x1 + 24*x2 <= 155)
m.addConstr(21*x0 + 24*x1 + 9*x2 <= 92)
m.addConstr(15*x0 + 21*x2 >= 27)
m.addConstr(24*x1 + 21*x2 >= 37)
m.addConstr(15*x0 + 24*x1 + 21*x2 >= 22)
m.addConstr(16*x0 + 24*x1 >= 37)
m.addConstr(24*x1 + 24*x2 >= 22)
m.addConstr(16*x0 + 24*x1 + 24*x2 >= 44)
m.addConstr(21*x0 + 24*x1 + 9*x2 >= 23)
m.addConstr(15*x0 + 24*x1 + 21*x2 <= 110)
m.addConstr(15*x0 + 21*x2 <= 59)
m.addConstr(24*x1 + 21*x2 <= 110)
m.addConstr(21*x0 + 22*x1 + 7*x2 <= 197)
m.addConstr(21*x0 + 22*x1 <= 190)
m.addConstr(21*x0 + 22*x1 + 7*x2 <= 66)
m.addConstr(16*x0 + 24*x1 + 24*x2 <= 147)
m.addConstr(24*x1 + 24*x2 <= 140)
m.addConstr(16*x0 + 24*x1 <= 53)
m.addConstr(16*x0 + 24*x1 + 24*x2 <= 53)
m.addConstr(21*x0 + 9*x2 <= 81)
m.addConstr(21*x0 + 24*x1 <= 69)
m.addConstr(21*x0 + 24*x1 + 9*x2 <= 69)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("SOC operators: ", x0.varValue)
    print("automatic alerts: ", x1.varValue)
    print("system administrators: ", x2.varValue)
else:
    print("The model is infeasible")
```