## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'security engineers' and 'patches per day'. Let's denote 'security engineers' as $x_1$ and 'patches per day' as $x_2$. The objective function to minimize is $9.0x_1 + 2.1x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
1. $0.63x_1 + 3.53x_2 \geq 16$ (dollar cost constraint)
2. $0.63x_1 + 3.53x_2 \leq 47$ (dollar cost upper bound constraint)
3. $2.84x_1 + 1.26x_2 \geq 36$ (bandwidth constraint)
4. $2.84x_1 + 1.26x_2 \leq 184$ (bandwidth upper bound constraint)
5. $0.01x_1 + 3.75x_2 \geq 30$ (network integrity impact constraint)
6. $0.01x_1 + 3.75x_2 \leq 105$ (network integrity impact upper bound constraint)
7. $-2x_1 + x_2 \geq 0$ (additional constraint)
8. $x_1$ is an integer (integer constraint for security engineers)
9. $x_2$ is an integer (integer constraint for patches per day)

## 3: Convert the problem into a Gurobi model
We will use Gurobi to solve this optimization problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="security_engineers", vtype=gp.GRB.INTEGER)  # security engineers
x2 = m.addVar(name="patches_per_day", vtype=gp.GRB.INTEGER)  # patches per day

# Define the objective function
m.setObjective(9.0 * x1 + 2.1 * x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(0.63 * x1 + 3.53 * x2 >= 16)  # dollar cost constraint
m.addConstr(0.63 * x1 + 3.53 * x2 <= 47)  # dollar cost upper bound constraint
m.addConstr(2.84 * x1 + 1.26 * x2 >= 36)  # bandwidth constraint
m.addConstr(2.84 * x1 + 1.26 * x2 <= 184)  # bandwidth upper bound constraint
m.addConstr(0.01 * x1 + 3.75 * x2 >= 30)  # network integrity impact constraint
m.addConstr(0.01 * x1 + 3.75 * x2 <= 105)  # network integrity impact upper bound constraint
m.addConstr(-2 * x1 + x2 >= 0)  # additional constraint

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Security Engineers: {x1.varValue}")
    print(f"Patches per Day: {x2.varValue}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'security engineers'), ('x2', 'patches per day')],
    'objective_function': '9.0*x1 + 2.1*x2',
    'constraints': [
        '0.63*x1 + 3.53*x2 >= 16',
        '0.63*x1 + 3.53*x2 <= 47',
        '2.84*x1 + 1.26*x2 >= 36',
        '2.84*x1 + 1.26*x2 <= 184',
        '0.01*x1 + 3.75*x2 >= 30',
        '0.01*x1 + 3.75*x2 <= 105',
        '-2*x1 + x2 >= 0'
    ]
}
```