To solve the optimization problem described, we first need to define the symbolic representation of the variables and the objective function, followed by the constraints.

Let's denote:
- \(x_0\) as 'patches per day',
- \(x_1\) as 'pen testers',
- \(x_2\) as 'intrusion analysts'.

The objective function is given by: 
\[7.19 \cdot x_0 \cdot x_1 + 1.57 \cdot x_0 \cdot x_2 + 2.02 \cdot x_1^2 + 3.09 \cdot x_0 + 7.49 \cdot x_1\]

The constraints are:
- \(11.44x_0 + 11.11x_1 + 14.9x_2 \leq 84\) (total power consumption constraint),
- \(12.65x_0 + 0.78x_1 + 14.19x_2 \leq 155\) (total data integrity impact constraint),
- \(11.44x_0 + 14.9x_2 \leq 65\) (power consumption of patches per day and intrusion analysts),
- \(12.65x_0 + 14.19x_2 \leq 69\) (data integrity impact from patches per day and intrusion analysts),
- \(0.78x_1 + 14.19x_2 \leq 105\) (data integrity impact from pen testers and intrusion analysts),
- \(12.65x_0 + 0.78x_1 \leq 107\) (data integrity impact from patches per day and pen testers),
- \(12.65x_0 + 0.78x_1 + 14.19x_2 \leq 131\) (total data integrity impact constraint including all variables),
- \(x_0, x_1, x_2 \in \mathbb{Z}^+\) (non-negativity and integer constraints for all variables).

Symbolic representation in JSON format:
```json
{
    'sym_variables': [('x0', 'patches per day'), ('x1', 'pen testers'), ('x2', 'intrusion analysts')],
    'objective_function': '7.19*x0*x1 + 1.57*x0*x2 + 2.02*x1**2 + 3.09*x0 + 7.49*x1',
    'constraints': [
        '11.44*x0 + 11.11*x1 + 14.9*x2 <= 84',
        '12.65*x0 + 0.78*x1 + 14.19*x2 <= 155',
        '11.44*x0 + 14.9*x2 <= 65',
        '12.65*x0 + 14.19*x2 <= 69',
        '0.78*x1 + 14.19*x2 <= 105',
        '12.65*x0 + 0.78*x1 <= 107',
        '12.65*x0 + 0.78*x1 + 14.19*x2 <= 131'
    ]
}
```

Now, let's implement this problem using Gurobi Python:

```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Define the variables
x0 = m.addVar(vtype=GRB.INTEGER, name="patches_per_day")
x1 = m.addVar(vtype=GRB.INTEGER, name="pen_testers")
x2 = m.addVar(vtype=GRB.INTEGER, name="intrusion_analysts")

# Set the objective function
m.setObjective(7.19*x0*x1 + 1.57*x0*x2 + 2.02*x1**2 + 3.09*x0 + 7.49*x1, GRB.MAXIMIZE)

# Add constraints
m.addConstr(11.44*x0 + 11.11*x1 + 14.9*x2 <= 84)
m.addConstr(12.65*x0 + 0.78*x1 + 14.19*x2 <= 155)
m.addConstr(11.44*x0 + 14.9*x2 <= 65)
m.addConstr(12.65*x0 + 14.19*x2 <= 69)
m.addConstr(0.78*x1 + 14.19*x2 <= 105)
m.addConstr(12.65*x0 + 0.78*x1 <= 107)
m.addConstr(12.65*x0 + 0.78*x1 + 14.19*x2 <= 131)

# Optimize the model
m.optimize()

# Print the results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")

print("Obj:", m.objVal)
```