To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

### Symbolic Representation:

- **Variables:**
  - $x_1$: Number of security onions
  - $x_2$: Number of pen testers

- **Objective Function:**
  - Minimize $7.64x_1 + 2.51x_2$

- **Constraints:**
  1. Network integrity impact constraint (minimum): $7x_1 + 11x_2 \geq 12$
  2. Network integrity impact constraint (maximum): $7x_1 + 11x_2 \leq 60$
  3. Data integrity impact constraint (minimum): $10x_1 + 5x_2 \geq 8$
  4. Data integrity impact constraint (maximum): $10x_1 + 5x_2 \leq 32$
  5. Additional linear constraint: $3x_1 - 8x_2 \geq 0$
  6. Non-negativity and integer constraints:
     - $x_1, x_2 \geq 0$ (since negative numbers of items don't make sense)
     - $x_1, x_2 \in \mathbb{Z}$ (integer constraint for non-fractional numbers)

### Symbolic Representation in JSON Format:

```json
{
    'sym_variables': [('x1', 'security onions'), ('x2', 'pen testers')],
    'objective_function': '7.64*x1 + 2.51*x2',
    'constraints': [
        '7*x1 + 11*x2 >= 12', 
        '7*x1 + 11*x2 <= 60', 
        '10*x1 + 5*x2 >= 8', 
        '10*x1 + 5*x2 <= 32', 
        '3*x1 - 8*x2 >= 0',
        'x1 >= 0', 
        'x2 >= 0'
    ]
}
```

### Gurobi Code:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="security_onions")
x2 = m.addVar(vtype=GRB.INTEGER, name="pen_testers")

# Set the objective function
m.setObjective(7.64*x1 + 2.51*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(7*x1 + 11*x2 >= 12, "network_integrity_min")
m.addConstr(7*x1 + 11*x2 <= 60, "network_integrity_max")
m.addConstr(10*x1 + 5*x2 >= 8, "data_integrity_min")
m.addConstr(10*x1 + 5*x2 <= 32, "data_integrity_max")
m.addConstr(3*x1 - 8*x2 >= 0, "additional_constraint")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Security Onions: {x1.x}")
    print(f"Pen Testers: {x2.x}")
else:
    print("No optimal solution found")
```