To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables for the quantities of interest (light infantry companies and mechanized infantry companies), formulating the objective function using these variables, and then expressing all constraints in terms of these variables.

### Symbolic Representation

Let's define:
- \(x_1\) as the number of light infantry companies,
- \(x_2\) as the number of mechanized infantry companies.

The objective function is to maximize \(5.17x_1 + 6.54x_2\).

Constraints based on the problem description are:
1. Logistics footprint constraint: \(4x_1 + 11x_2 \geq 14\),
2. Logistical capacity constraint: \(5x_1 + 11x_2 \geq 20\),
3. Defensive capability rating constraint: \(8x_1 + 8x_2 \geq 17\),
4. Mixed constraint: \(2x_1 - x_2 \geq 0\),
5. Total logistics footprint upper bound: \(4x_1 + 11x_2 \leq 31\),
6. Total logistical capacity upper bound: \(5x_1 + 11x_2 \leq 64\),
7. Total defensive capability rating upper bound: \(8x_1 + 8x_2 \leq 31\).

Since both \(x_1\) and \(x_2\) must be whole numbers, we also have:
- \(x_1 \in \mathbb{Z}^+\),
- \(x_2 \in \mathbb{Z}^+\).

### Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'light infantry companies'), ('x2', 'mechanized infantry companies')],
    'objective_function': '5.17*x1 + 6.54*x2',
    'constraints': [
        '4*x1 + 11*x2 >= 14',
        '5*x1 + 11*x2 >= 20',
        '8*x1 + 8*x2 >= 17',
        '2*x1 - x2 >= 0',
        '4*x1 + 11*x2 <= 31',
        '5*x1 + 11*x2 <= 64',
        '8*x1 + 8*x2 <= 31'
    ]
}
```

### Gurobi Code

```python
from gurobipy import *

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

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

# Set objective function
m.setObjective(5.17*x1 + 6.54*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(4*x1 + 11*x2 >= 14, "logistics_footprint_min")
m.addConstr(5*x1 + 11*x2 >= 20, "logistical_capacity_min")
m.addConstr(8*x1 + 8*x2 >= 17, "defensive_capability_rating_min")
m.addConstr(2*x1 - x2 >= 0, "mixed_constraint")
m.addConstr(4*x1 + 11*x2 <= 31, "logistics_footprint_max")
m.addConstr(5*x1 + 11*x2 <= 64, "logistical_capacity_max")
m.addConstr(8*x1 + 8*x2 <= 31, "defensive_capability_rating_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Light Infantry Companies: {x1.x}")
    print(f"Mechanized Infantry Companies: {x2.x}")
else:
    print("No optimal solution found")
```