## Step 1: Define the symbolic representation of the variables
The variables are 'pen testers', 'security onions', and 'network administrators', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $9.23x_0^2 + 6.65x_0x_2 + 8.65x_1^2 + 3.85x_1x_2 + 2.11x_2^2 + 2.97x_0$.

## Step 3: List the constraints in symbolic notation
1. $3x_0 + 4x_1 + 5x_2 \leq 44$ (network integrity impact)
2. $7x_0 + 8x_1 + 4x_2 \leq 53$ (available bandwidth impact)
3. $5x_0 + x_1 + 4x_2 \leq 49$ (power consumption)
4. $x_0 + x_1 + 4x_2 \leq 68$ (dollar cost)
5. $x_0^2 + x_1^2 \geq 15$ (minimum bandwidth used)
6. $x_1^2 + x_2^2 \geq 16$ (power consumption of security onions and network administrators)
7. $5x_0 + x_1 + 4x_2 \geq 15$ (power consumption contribution)
8. $x_1 + 4x_2 \geq 7$ (minimum spend on security onions and network administrators)
9. $6x_0^2 - x_2^2 \geq 0$ (pen testers and network administrators constraint)
10. $3x_0 + 5x_2 \leq 38$ (network integrity impact from pen testers and network administrators)
11. $3x_0 + 4x_1 \leq 39$ (network integrity impact from pen testers and security onions)
12. $3x_0 + 4x_1 + 5x_2 \leq 39$ (total network integrity impact)
13. $x_0^2 + x_1^2 \leq 46$ (bandwidth from pen testers and security onions)
14. $7x_0 + 8x_1 + 4x_2 \leq 46$ (maximum available bandwidth)
15. $5x_0^2 + x_1^2 \leq 44$ (power consumption of pen testers and security onions)
16. $x_1^2 + 4x_2^2 \leq 17$ (power consumption of security onions and network administrators)
17. $5x_0 + x_1 + 4x_2 \leq 17$ (power consumption limit)
18. $x_0^2 + x_1^2 \leq 27$ (cost of pen testers and security onions)
19. $x_1^2 + 4x_2^2 \leq 32$ (cost of security onions and network administrators)
20. $x_0^2 + x_1^2 + 4x_2^2 \leq 67$ (total cost limit)
21. $x_0 + x_1 + 4x_2 \leq 67$ (total cost limit)
22. $x_0, x_1, x_2 \in \mathbb{Z}$ (integer constraints)

## Step 4: Create the symbolic representation dictionary
```json
{
    'sym_variables': [
        ('x0', 'pen testers'), 
        ('x1', 'security onions'), 
        ('x2', 'network administrators')
    ], 
    'objective_function': '9.23*x0^2 + 6.65*x0*x2 + 8.65*x1^2 + 3.85*x1*x2 + 2.11*x2^2 + 2.97*x0', 
    'constraints': [
        '3*x0 + 4*x1 + 5*x2 <= 44',
        '7*x0 + 8*x1 + 4*x2 <= 53',
        '5*x0 + x1 + 4*x2 <= 49',
        'x0 + x1 + 4*x2 <= 68',
        'x0^2 + x1^2 >= 15',
        'x1^2 + x2^2 >= 16',
        '5*x0 + x1 + 4*x2 >= 15',
        'x1 + 4*x2 >= 7',
        '6*x0^2 - x2^2 >= 0',
        '3*x0 + 5*x2 <= 38',
        '3*x0 + 4*x1 <= 39',
        '3*x0 + 4*x1 + 5*x2 <= 39',
        'x0^2 + x1^2 <= 46',
        '7*x0 + 8*x1 + 4*x2 <= 46',
        '5*x0^2 + x1^2 <= 44',
        'x1^2 + 4*x2^2 <= 17',
        '5*x0 + x1 + 4*x2 <= 17',
        'x0^2 + x1^2 <= 27',
        'x1^2 + 4*x2^2 <= 32',
        'x0^2 + x1^2 + 4*x2^2 <= 67',
        'x0 + x1 + 4*x2 <= 67'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name='pen_testers', vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name='security_onions', vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name='network_administrators', vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(9.23*x0**2 + 6.65*x0*x2 + 8.65*x1**2 + 3.85*x1*x2 + 2.11*x2**2 + 2.97*x0, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x0 + 4*x1 + 5*x2 <= 44)
m.addConstr(7*x0 + 8*x1 + 4*x2 <= 53)
m.addConstr(5*x0 + x1 + 4*x2 <= 49)
m.addConstr(x0 + x1 + 4*x2 <= 68)
m.addConstr(x0**2 + x1**2 >= 15)
m.addConstr(x1**2 + x2**2 >= 16)
m.addConstr(5*x0 + x1 + 4*x2 >= 15)
m.addConstr(x1 + 4*x2 >= 7)
m.addConstr(6*x0**2 - x2**2 >= 0)
m.addConstr(3*x0 + 5*x2 <= 38)
m.addConstr(3*x0 + 4*x1 <= 39)
m.addConstr(3*x0 + 4*x1 + 5*x2 <= 39)
m.addConstr(x0**2 + x1**2 <= 46)
m.addConstr(7*x0 + 8*x1 + 4*x2 <= 46)
m.addConstr(5*x0**2 + x1**2 <= 44)
m.addConstr(x1**2 + 4*x2**2 <= 17)
m.addConstr(5*x0 + x1 + 4*x2 <= 17)
m.addConstr(x0**2 + x1**2 <= 27)
m.addConstr(x1**2 + 4*x2**2 <= 32)
m.addConstr(x0**2 + x1**2 + 4*x2**2 <= 67)
m.addConstr(x0 + x1 + 4*x2 <= 67)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('pen testers: ', x0.varValue)
    print('security onions: ', x1.varValue)
    print('network administrators: ', x2.varValue)
else:
    print('No solution found')
```