## Step 1: Define the symbolic representation of the variables
The variables are 'security engineers', 'automatic alerts', and 'patches per day', 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 minimize is $3x_1^2 + 3x_1x_3 + 3x_2^2 + 3x_2x_3 + 2x_3^2 + 6x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $10x_1 \geq 0$ (data confidentiality impact of security engineers, but it seems there's a direct value given, not a range, so we consider it as $x_1 \geq 0$ and $x_1 \leq \infty$ but with a specific value of impact),
2. $23x_2$ (data confidentiality impact of automatic alerts),
3. $1x_3$ (data confidentiality impact of patches per day),
4. $10x_1 + 23x_2 \geq 21$ (total combined data confidentiality impact from security engineers and automatic alerts),
5. $10^2 + 1^2 \geq 35$ is not a constraint but a given, however $10^2x_1^2 + 1^2x_3^2 \geq 35$ seems to be misinterpreted. The correct interpretation is $100x_1^2 + x_3^2 \geq 35$,
6. $10x_1 + 23x_2 + x_3 \geq 35$ (total combined data confidentiality impact),
7. $10x_1 - x_3 \geq 0$ (relationship between security engineers and patches per day).

## 4: Correct and Clarify Constraints
Given:
- The data confidentiality impact of security engineers is 10.
- Automatic alerts have a data confidentiality impact of 23 each.
- Patches per day each have a data confidentiality impact of 1.

Correct constraints:
1. $10x_1 + 23x_2 + x_3 \geq 35$
2. $10x_1^2 + x_3^2 \geq 35$
3. $10x_1 + 23x_2 \geq 21$
4. $10x_1 - x_3 \geq 0$

## 5: Symbolic Representation
```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',
    '100*x1^2 + x3^2 >= 35',
    '10*x1 + 23*x2 + x3 >= 35',
    '10*x1 - x3 >= 0',
    'x1 >= 0', 'x2 >= 0', 'x3 >= 0',
    'x1 % 1 == 0', 'x2 % 1 == 0', 'x3 % 1 == 0'
]
}
```

## 6: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(name="security_engineers", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="automatic_alerts", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="patches_per_day", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(3*x1**2 + 3*x1*x3 + 3*x2**2 + 3*x2*x3 + 2*x3**2 + 6*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10*x1 + 23*x2 >= 21)
    model.addConstr(100*x1**2 + x3**2 >= 35)
    model.addConstr(10*x1 + 23*x2 + x3 >= 35)
    model.addConstr(10*x1 - x3 >= 0)

    # Solve the model
    model.optimize()

    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Security Engineers: {x1.varValue}")
        print(f"Automatic Alerts: {x2.varValue}")
        print(f"Patches per Day: {x3.varValue}")
        print(f"Objective Function Value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```