## Step 1: Define the symbolic representation of the variables
The variables are 'Mbps bandwidth allocated to monitoring' and 'intrusion analysts'. Let's denote them as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $2x_1^2 + 3x_1x_2 + 2x_2^2 + 2x_1 + 7x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $19x_1 \leq 93$
- $19x_1 \leq 90$
- $13x_1 \leq 268$
- $22x_1 \leq 149$
- $21x_2 \leq 93$
- $9x_2 \leq 90$
- $13x_2 \leq 268$
- $6x_2 \leq 149$
- $19x_1 + 21x_2 \geq 33$
- $19x_1 + 21x_2 \geq 33$
- $19x_1 + 9x_2 \geq 31$
- $19x_1 + 9x_2 \geq 31$
- $13x_1 + 13x_2 \geq 90$
- $22x_1 + 6x_2 \geq 62$
- $22x_1 + 6x_2 \geq 62$
- $10x_1 - 6x_2 \geq 0$
- $19x_1 + 21x_2 \leq 90$
- $(19x_1)^2 + (9x_2)^2 \leq 57$
- $22x_1 + 6x_2 \leq 114$
- $x_1 \in \mathbb{Z}$
- $x_2 \in \mathbb{Z}$

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name="Mbps_bandwidth_allocated_to_monitoring", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="intrusion_analysts", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(2*x1**2 + 3*x1*x2 + 2*x2**2 + 2*x1 + 7*x2, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(19*x1 <= 93)
m.addConstr(19*x1 <= 90)
m.addConstr(13*x1 <= 268)
m.addConstr(22*x1 <= 149)
m.addConstr(21*x2 <= 93)
m.addConstr(9*x2 <= 90)
m.addConstr(13*x2 <= 268)
m.addConstr(6*x2 <= 149)
m.addConstr(19*x1 + 21*x2 >= 33)
m.addConstr(19*x1 + 9*x2 >= 31)
m.addConstr(13*x1 + 13*x2 >= 90)
m.addConstr(22*x1 + 6*x2 >= 62)
m.addConstr(10*x1 - 6*x2 >= 0)
m.addConstr(19*x1 + 21*x2 <= 90)
m.addConstr((19*x1)**2 + (9*x2)**2 <= 57)
m.addConstr(22*x1 + 6*x2 <= 114)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Mbps bandwidth allocated to monitoring:", x1.varValue)
    print("intrusion analysts:", x2.varValue)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found.")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'Mbps bandwidth allocated to monitoring'), ('x2', 'intrusion analysts')],
    'objective_function': '2*x1^2 + 3*x1*x2 + 2*x2^2 + 2*x1 + 7*x2',
    'constraints': [
        '19*x1 <= 93',
        '19*x1 <= 90',
        '13*x1 <= 268',
        '22*x1 <= 149',
        '21*x2 <= 93',
        '9*x2 <= 90',
        '13*x2 <= 268',
        '6*x2 <= 149',
        '19*x1 + 21*x2 >= 33',
        '19*x1 + 9*x2 >= 31',
        '13*x1 + 13*x2 >= 90',
        '22*x1 + 6*x2 >= 62',
        '10*x1 - 6*x2 >= 0',
        '19*x1 + 21*x2 <= 90',
        '(19*x1)^2 + (9*x2)^2 <= 57',
        '22*x1 + 6*x2 <= 114',
        'x1 ∈ ℤ',
        'x2 ∈ ℤ'
    ]
}
```