## Step 1: Define the symbolic representation of the variables
The variables are 'patches per day', 'pen testers', and 'intrusion analysts', which we will denote as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $7.19 \cdot x_1 \cdot x_2 + 1.57 \cdot x_1 \cdot x_3 + 2.02 \cdot x_2^2 + 3.09 \cdot x_1 + 7.49 \cdot x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $11.44x_1 + 11.11x_2 + 14.9x_3 \leq 84$ (power consumption constraint)
- $12.65x_1 + 0.78x_2 + 14.19x_3 \leq 155$ (data integrity impact constraint)
- $x_1 + x_3 \leq 65 / 11.44$ is not correct, instead we have $11.44x_1 + 14.9x_3 \leq 65$ (power consumption of patches per day and intrusion analysts)
- $12.65x_1 + 14.19x_3 \leq 69$ (data integrity impact of patches per day and intrusion analysts)
- $0.78x_2 + 14.19x_3 \leq 105$ (data integrity impact of pen testers and intrusion analysts)
- $12.65x_1 + 0.78x_2 \leq 107$ (data integrity impact of patches per day and pen testers)
- $12.65x_1 + 0.78x_2 + 14.19x_3 \leq 131$ (total data integrity impact)
- $x_1 \in \mathbb{Z}$ (patches per day must be a whole number)
- $x_2 \in \mathbb{Z}$ (pen testers must be a whole number)
- $x_3 \in \mathbb{Z}$ (intrusion analysts must be a whole number)

## 4: Correct and simplify constraints for accurate representation
Correcting and simplifying:
- Power consumption: $11.44x_1 + 11.11x_2 + 14.9x_3 \leq 84$
- Data integrity: $12.65x_1 + 0.78x_2 + 14.19x_3 \leq 155$
- Patches per day and intrusion analysts power: $11.44x_1 + 14.9x_3 \leq 65$
- Patches per day and intrusion analysts data integrity: $12.65x_1 + 14.19x_3 \leq 69$
- Pen testers and intrusion analysts data integrity: $0.78x_2 + 14.19x_3 \leq 105$
- Patches per day and pen testers data integrity: $12.65x_1 + 0.78x_2 \leq 107$
- Total data integrity: $12.65x_1 + 0.78x_2 + 14.19x_3 \leq 131$

## 5: Write down the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'patches per day'), ('x2', 'pen testers'), ('x3', 'intrusion analysts')],
    'objective_function': '7.19 * x1 * x2 + 1.57 * x1 * x3 + 2.02 * x2^2 + 3.09 * x1 + 7.49 * x2',
    'constraints': [
        '11.44 * x1 + 11.11 * x2 + 14.9 * x3 <= 84',
        '12.65 * x1 + 0.78 * x2 + 14.19 * x3 <= 155',
        '11.44 * x1 + 14.9 * x3 <= 65',
        '12.65 * x1 + 14.19 * x3 <= 69',
        '0.78 * x2 + 14.19 * x3 <= 105',
        '12.65 * x1 + 0.78 * x2 <= 107',
        '12.65 * x1 + 0.78 * x2 + 14.19 * x3 <= 131',
        'x1 ∈ ℤ',
        'x2 ∈ ℤ',
        'x3 ∈ ℤ'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```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="pen_testers", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="intrusion_analysts", vtype=gurobi.GRB.INTEGER)

    # Define objective function
    model.setObjective(7.19 * x1 * x2 + 1.57 * x1 * x3 + 2.02 * x2**2 + 3.09 * x1 + 7.49 * x2, gurobi.GRB.MAXIMIZE)

    # Define constraints
    model.addConstr(11.44 * x1 + 11.11 * x2 + 14.9 * x3 <= 84)
    model.addConstr(12.65 * x1 + 0.78 * x2 + 14.19 * x3 <= 155)
    model.addConstr(11.44 * x1 + 14.9 * x3 <= 65)
    model.addConstr(12.65 * x1 + 14.19 * x3 <= 69)
    model.addConstr(0.78 * x2 + 14.19 * x3 <= 105)
    model.addConstr(12.65 * x1 + 0.78 * x2 <= 107)
    model.addConstr(12.65 * x1 + 0.78 * x2 + 14.19 * x3 <= 131)

    # 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("Pen testers: ", x2.varValue)
        print("Intrusion analysts: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```