## Step 1: Define the symbolic representation of the variables
The variables are: 
- intrusion analysts: $x_1$
- security engineers: $x_2$
- security onions: $x_3$
- patches per day: $x_4$

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is: 
$4x_1^2 + 7x_1x_2 + 8x_1x_3 + x_1x_4 + 5x_2^2 + 6x_2x_3 + 3x_2x_4 + 5x_3^2 + 2x_4^2 + 7x_1 + 9x_2 + 2x_3 + 2x_4$

## Step 3: List the constraints in symbolic notation
Constraints:
- $3.06x_1 \leq 380$ (data integrity impact of intrusion analysts, but it seems like it should be an equality or another type of constraint, however, based on given data: $x_1 \geq 0$ and $3.06$ is a coefficient, not a constraint directly)
- $7.97x_1 \leq 562$ (data confidentiality impact of intrusion analysts)
- $9.97x_2 \leq 380$ 
- $1.85x_2 \leq 562$ 
- $9.62x_3 \leq 380$ 
- $4.1x_3 \leq 562$ 
- $8.77x_4 \leq 380$ 
- $2.95x_4 \leq 562$ 
- $3.06x_1 + 8.77x_4 \geq 88$ 
- $3.06^2x_1^2 + 9.62^2x_3^2 \geq 43$ 
- $9.62^2x_3^2 + 8.77^2x_4^2 \geq 46$ 
- $3.06x_1 + 9.97x_2 + 8.77x_4 \geq 60$ 
- $9.97x_2 + 9.62x_3 + 8.77x_4 \geq 60$ 
- $3.06x_1 + 9.62x_3 + 8.77x_4 \geq 60$ 
- $3.06x_1 + 9.97x_2 + 9.62x_3 \geq 60$ 
- $3.06x_1 + 9.97x_2 + 8.77x_4 \geq 61$ 
- $9.97x_2 + 9.62x_3 + 8.77x_4 \geq 61$ 
- $3.06x_1 + 9.62x_3 + 8.77x_4 \geq 61$ 
- $3.06^2x_1^2 + 9.97^2x_2^2 + 9.62^2x_3^2 \geq 61$ 
- $3.06x_1 + 9.97x_2 + 8.77x_4 \geq 84$ 
- $9.97x_2 + 9.62x_3 + 8.77x_4 \geq 84$ 
- $3.06x_1 + 9.62x_3 + 8.77x_4 \geq 84$ 
- $3.06x_1 + 9.97x_2 + 9.62x_3 \geq 84$ 
- $3.06x_1 + 9.97x_2 + 8.77x_4 \geq 69$ 
- $9.97x_2 + 9.62x_3 + 8.77x_4 \geq 69$ 
- $3.06x_1 + 9.62x_3 + 8.77x_4 \geq 69$ 
- $3.06x_1 + 9.97x_2 + 9.62x_3 \geq 69$ 
- $3.06x_1 + 9.97x_2 + 9.62x_3 + 8.77x_4 \geq 69$ 
- $4.1x_3 + 2.95x_4 \geq 105$ 
- $7.97x_1 + 2.95x_4 \geq 88$ 
- $1.85^2x_2^2 + 4.1^2x_3^2 \geq 109$ 
- $7.97x_1 + 1.85x_2 + 4.1x_3 + 2.95x_4 \geq 109$ 
- $9.62^2x_3^2 + 8.77^2x_4^2 \leq 231$ 
- $3.06x_1 + 8.77x_4 \leq 324$ 
- $9.97x_2 + 9.62x_3 \leq 166$ 
- $9.97x_2 + 9.62x_3 + 8.77x_4 \leq 232$ 
- $3.06x_1 + 9.97x_2 + 9.62x_3 \leq 334$ 
- $3.06^2x_1^2 + 9.97^2x_2^2 + 8.77^2x_4^2 \leq 97$ 
- $x_1, x_2, x_3, x_4$ are integers.

## 4: Converting problem into Gurobi code

```python
import gurobi

# Define the model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(vtype=gurobi.GRB.INTEGER, name="intrusion_analysts")
x2 = m.addVar(vtype=gurobi.GRB.INTEGER, name="security_engineers")
x3 = m.addVar(vtype=gurobi.GRB.INTEGER, name="security_onions")
x4 = m.addVar(vtype=gurobi.GRB.INTEGER, name="patches_per_day")

# Objective function
m.setObjective(4*x1**2 + 7*x1*x2 + 8*x1*x3 + x1*x4 + 5*x2**2 + 6*x2*x3 + 3*x2*x4 + 5*x3**2 + 2*x4**2 + 7*x1 + 9*x2 + 2*x3 + 2*x4, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(3.06*x1 <= 380, name="data_integrity_impact_intrusion_analysts")
m.addConstr(7.97*x1 <= 562, name="data_confidentiality_impact_intrusion_analysts")
m.addConstr(9.97*x2 <= 380, name="data_integrity_impact_security_engineers")
m.addConstr(1.85*x2 <= 562, name="data_confidentiality_impact_security_engineers")
m.addConstr(9.62*x3 <= 380, name="data_integrity_impact_security_onions")
m.addConstr(4.1*x3 <= 562, name="data_confidentiality_impact_security_onions")
m.addConstr(8.77*x4 <= 380, name="data_integrity_impact_patches_per_day")
m.addConstr(2.95*x4 <= 562, name="data_confidentiality_impact_patches_per_day")

m.addConstr(3.06*x1 + 8.77*x4 >= 88, name="total_data_integrity_impact_intrusion_analysts_patches")
m.addConstr(3.06**2*x1**2 + 9.62**2*x3**2 >= 43, name="total_data_integrity_impact_intrusion_analysts_security_onions")
m.addConstr(9.62**2*x3**2 + 8.77**2*x4**2 >= 46, name="total_data_integrity_impact_security_onions_patches")

m.addConstr(3.06*x1 + 9.97*x2 + 8.77*x4 >= 60, name="total_data_integrity_impact_intrusion_analysts_security_engineers_patches")
m.addConstr(9.97*x2 + 9.62*x3 + 8.77*x4 >= 60, name="total_data_integrity_impact_security_engineers_security_onions_patches")
m.addConstr(3.06*x1 + 9.62*x3 + 8.77*x4 >= 60, name="total_data_integrity_impact_intrusion_analysts_security_onions_patches")
m.addConstr(3.06*x1 + 9.97*x2 + 9.62*x3 >= 60, name="total_data_integrity_impact_intrusion_analysts_security_engineers_security_onions")

m.addConstr(3.06*x1 + 9.97*x2 + 8.77*x4 >= 61, name="total_data_integrity_impact_intrusion_analysts_security_engineers_patches_61")
m.addConstr(9.97*x2 + 9.62*x3 + 8.77*x4 >= 61, name="total_data_integrity_impact_security_engineers_security_onions_patches_61")
m.addConstr(3.06*x1 + 9.62*x3 + 8.77*x4 >= 61, name="total_data_integrity_impact_intrusion_analysts_security_onions_patches_61")

m.addConstr(3.06**2*x1**2 + 9.97**2*x2**2 + 9.62**2*x3**2 >= 61, name="total_data_integrity_impact_squared")

m.addConstr(3.06*x1 + 9.97*x2 + 8.77*x4 >= 84, name="total_data_integrity_impact_84")
m.addConstr(9.97*x2 + 9.62*x3 + 8.77*x4 >= 84, name="total_data_integrity_impact_84_2")
m.addConstr(3.06*x1 + 9.62*x3 + 8.77*x4 >= 84, name="total_data_integrity_impact_84_3")
m.addConstr(3.06*x1 + 9.97*x2 + 9.62*x3 >= 84, name="total_data_integrity_impact_84_4")

m.addConstr(4.1*x3 + 2.95*x4 >= 105, name="data_confidentiality_impact_security_onions_patches")
m.addConstr(7.97*x1 + 2.95*x4 >= 88, name="data_confidentiality_impact_intrusion_analysts_patches")
m.addConstr(1.85**2*x2**2 + 4.1**2*x3**2 >= 109, name="data_confidentiality_impact_security_engineers_security_onions")
m.addConstr(7.97*x1 + 1.85*x2 + 4.1*x3 + 2.95*x4 >= 109, name="data_confidentiality_impact_all")

m.addConstr(9.62**2*x3**2 + 8.77**2*x4**2 <= 231, name="data_integrity_impact_security_onions_patches_max")
m.addConstr(3.06*x1 + 8.77*x4 <= 324, name="data_integrity_impact_intrusion_analysts_patches_max")
m.addConstr(9.97*x2 + 9.62*x3 <= 166, name="data_integrity_impact_security_engineers_security_onions_max")
m.addConstr(9.97*x2 + 9.62*x3 + 8.77*x4 <= 232, name="data_integrity_impact_security_engineers_security_onions_patches_max")
m.addConstr(3.06*x1 + 9.97*x2 + 9.62*x3 <= 334, name="data_integrity_impact_intrusion_analysts_security_engineers_security_onions_max")
m.addConstr(3.06**2*x1**2 + 9.97**2*x2**2 + 8.77**2*x4**2 <= 97, name="data_integrity_impact_squared_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Intrusion Analysts: ", x1.varValue)
    print("Security Engineers: ", x2.varValue)
    print("Security Onions: ", x3.varValue)
    print("Patches per Day: ", x4.varValue)
else:
    print("No solution found")
```

## 5: Symbolic Representation

```json
{
    'sym_variables': [
        ('x1', 'intrusion analysts'),
        ('x2', 'security engineers'),
        ('x3', 'security onions'),
        ('x4', 'patches per day')
    ],
    'objective_function': '4*x1^2 + 7*x1*x2 + 8*x1*x3 + x1*x4 + 5*x2^2 + 6*x2*x3 + 3*x2*x4 + 5*x3^2 + 2*x4^2 + 7*x1 + 9*x2 + 2*x3 + 2*x4',
    'constraints': [
        '3.06*x1 <= 380',
        '7.97*x1 <= 562',
        '9.97*x2 <= 380',
        '1.85*x2 <= 562',
        '9.62*x3 <= 380',
        '4.1*x3 <= 562',
        '8.77*x4 <= 380',
        '2.95*x4 <= 562',
        '3.06*x1 + 8.77*x4 >= 88',
        '3.06^2*x1^2 + 9.62^2*x3^2 >= 43',
        '9.62^2*x3^2 + 8.77^2*x4^2 >= 46',
        '3.06*x1 + 9.97*x2 + 8.77*x4 >= 60',
        '9.97*x2 + 9.62*x3 + 8.77*x4 >= 60',
        '3.06*x1 + 9.62*x3 + 8.77*x4 >= 60',
        '3.06*x1 + 9.97*x2 + 9.62*x3 >= 60',
        '4.1*x3 + 2.95*x4 >= 105',
        '7.97*x1 + 2.95*x4 >= 88',
        '1.85^2*x2^2 + 4.1^2*x3^2 >= 109',
        '7.97*x1 + 1.85*x2 + 4.1*x3 + 2.95*x4 >= 109',
        '9.62^2*x3^2 + 8.77^2*x4^2 <= 231',
        '3.06*x1 + 8.77*x4 <= 324',
        '9.97*x2 + 9.62*x3 <= 166',
        '9.97*x2 + 9.62*x3 + 8.77*x4 <= 232',
        '3.06*x1 + 9.97*x2 + 9.62*x3 <= 334',
        '3.06^2*x1^2 + 9.97^2*x2^2 + 8.77^2*x4^2 <= 97'
    ]
}
```