## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and the objective function based on the given problem description.

- Let $x_0$ be the number of 'network administrators' and $x_1$ be the number of 'intrusion analysts'.

## Step 2: Translate the problem into a symbolic optimization problem
The objective function to minimize is $1.55x_0 + 8.05x_1$.

## Step 3: List all constraints in symbolic form
Constraints:
1. $0.29x_0 + 3.64x_1 \geq 12$
2. $0.29x_0 + 3.64x_1 \geq 12$ (same as the first, redundant)
3. $1.96x_0 + 4.3x_1 \geq 6$
4. $1.96x_0 + 4.3x_1 \geq 6$ (same as the third, redundant)
5. $0.04x_0 + 1.27x_1 \geq 3$
6. $0.04x_0 + 1.27x_1 \geq 3$ (same as the fifth, redundant)
7. $2x_0 - 5x_1 \geq 0$
8. $0.29x_0 + 3.64x_1 \leq 25$
9. $1.96x_0 + 4.3x_1 \leq 22$
10. $0.04x_0 + 1.27x_1 \leq 15$
11. $x_0 \geq 0$ and $x_0$ is an integer
12. $x_1 \geq 0$ and $x_1$ is an integer

## 4: Remove redundant constraints
After reviewing, we can see that there are redundant constraints. The simplified list without redundancy is:
1. $0.29x_0 + 3.64x_1 \geq 12$
2. $1.96x_0 + 4.3x_1 \geq 6$
3. $0.04x_0 + 1.27x_1 \geq 3$
4. $2x_0 - 5x_1 \geq 0$
5. $0.29x_0 + 3.64x_1 \leq 25$
6. $1.96x_0 + 4.3x_1 \leq 22$
7. $0.04x_0 + 1.27x_1 \leq 15$
8. $x_0, x_1 \geq 0$ and are integers

## 5: Write down the symbolic representation
```json
{
'sym_variables': [('x0', 'network administrators'), ('x1', 'intrusion analysts')],
'objective_function': '1.55*x0 + 8.05*x1',
'constraints': [
    '0.29*x0 + 3.64*x1 >= 12',
    '1.96*x0 + 4.3*x1 >= 6',
    '0.04*x0 + 1.27*x1 >= 3',
    '2*x0 - 5*x1 >= 0',
    '0.29*x0 + 3.64*x1 <= 25',
    '1.96*x0 + 4.3*x1 <= 22',
    '0.04*x0 + 1.27*x1 <= 15',
    'x0 >= 0', 'x1 >= 0'
]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="network_administrators", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="intrusion_analysts", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(1.55 * x0 + 8.05 * x1, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(0.29 * x0 + 3.64 * x1 >= 12)
    model.addConstr(1.96 * x0 + 4.3 * x1 >= 6)
    model.addConstr(0.04 * x0 + 1.27 * x1 >= 3)
    model.addConstr(2 * x0 - 5 * x1 >= 0)
    model.addConstr(0.29 * x0 + 3.64 * x1 <= 25)
    model.addConstr(1.96 * x0 + 4.3 * x1 <= 22)
    model.addConstr(0.04 * x0 + 1.27 * x1 <= 15)

    # Non-negativity constraints
    model.addConstr(x0 >= 0)
    model.addConstr(x1 >= 0)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Network Administrators: {x0.varValue}")
        print(f"Intrusion Analysts: {x1.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```