To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using algebraic terms.

Let's denote:
- $x_1$ as the number of security engineers,
- $x_2$ as the number of automatic alerts,
- $x_3$ as the patches per day.

The objective function to minimize is given by: 
\[3x_1^2 + 3x_1x_3 + 3x_2^2 + 3x_2x_3 + 2x_3^2 + 6x_2\]

The constraints are:
1. Data confidentiality impact of security engineers is 10: $10x_1$
2. Automatic alerts have a data confidentiality impact of 23 each: $23x_2$
3. Patches per day have a data confidentiality impact of 1: $x_3$
4. The total combined data confidentiality impact from security engineers and automatic alerts should be at least 21: $10x_1 + 23x_2 \geq 21$
5. The total combined data confidentiality impact from security engineers squared, and patches per day squared must be as much or more than 35: $(10x_1)^2 + x_3^2 \geq 35$
6. The total combined data confidentiality impact from security engineers plus automatic alerts plus patches per day should be at minimum 35: $10x_1 + 23x_2 + x_3 \geq 35$
7. $10x_1 - x_3 \geq 0$
8. $x_1$ is an integer.
9. $x_2$ is non-negative and can be any real number but for practical purposes, we'll consider it as a continuous variable since no specific restriction to integers is mentioned.
10. $x_3$ must be an integer.

Given this information, the symbolic representation of the problem in JSON format is:
```json
{
  'sym_variables': [('x1', 'security engineers'), ('x2', 'automatic alerts'), ('x3', 'patches per day')],
  'objective_function': '3*x1**2 + 3*x1*x3 + 3*x2**2 + 3*x2*x3 + 2*x3**2 + 6*x2',
  'constraints': [
    '10*x1 + 23*x2 >= 21',
    '(10*x1)**2 + x3**2 >= 35',
    '10*x1 + 23*x2 + x3 >= 35',
    '10*x1 - x3 >= 0',
    'x1 == int(x1)',  # To ensure x1 is an integer
    'x3 == int(x3)'   # To ensure x3 is an integer
  ]
}
```

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

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(vtype=GRB.INTEGER, name="security_engineers")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="automatic_alerts", lb=0)
x3 = m.addVar(vtype=GRB.INTEGER, name="patches_per_day")

# Define the objective function
m.setObjective(3*x1**2 + 3*x1*x3 + 3*x2**2 + 3*x2*x3 + 2*x3**2 + 6*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(10*x1 + 23*x2 >= 21, name="confidentiality_impact_security_and_alerts")
m.addConstr((10*x1)**2 + x3**2 >= 35, name="security_and_patches_squared_impact")
m.addConstr(10*x1 + 23*x2 + x3 >= 35, name="total_confidentiality_impact")
m.addConstr(10*x1 - x3 >= 0, name="security_vs_patches")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Security Engineers: {x1.x}")
    print(f"Automatic Alerts: {x2.x}")
    print(f"Patches per Day: {x3.x}")
else:
    print("No optimal solution found.")
```