To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using mathematical notation.

Let's denote:
- $x_1$ as the number of reconnaissance troops,
- $x_2$ as the number of light infantry companies.

The objective function to maximize is: $9x_1 + 5x_2$

The constraints are:
1. The total combined fun factor from reconnaissance troops and light infantry companies should be equal to or greater than 45: $8.6x_1 + 2.79x_2 \geq 45$
2. $9x_1 - 5x_2 \geq 0$
3. The total combined fun factor from reconnaissance troops plus light infantry companies should be less than or equal to 83: $8.6x_1 + 2.79x_2 \leq 83$
4. $x_1$ must be an integer (non-fractional number of reconnaissance troops).
5. $x_2$ must be an integer (no non-integer number of light infantry companies).

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'reconnaissance troops'), ('x2', 'light infantry companies')],
    'objective_function': '9*x1 + 5*x2',
    'constraints': [
        '8.6*x1 + 2.79*x2 >= 45',
        '9*x1 - 5*x2 >= 0',
        '8.6*x1 + 2.79*x2 <= 83',
        'x1 == int(x1)',
        'x2 == int(x2)'
    ]
}
```

Now, let's implement this problem in Gurobi Python:

```python
from gurobipy import *

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

# Add variables to the model
x1 = m.addVar(vtype=GRB.INTEGER, name="reconnaissance_troops")
x2 = m.addVar(vtype=GRB.INTEGER, name="light_infantry_companies")

# Set the objective function
m.setObjective(9*x1 + 5*x2, GRB.MAXIMIZE)

# Add constraints to the model
m.addConstr(8.6*x1 + 2.79*x2 >= 45, "fun_factor_min")
m.addConstr(9*x1 - 5*x2 >= 0, "troops_vs_companies")
m.addConstr(8.6*x1 + 2.79*x2 <= 83, "fun_factor_max")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Reconnaissance troops: {x1.x}")
    print(f"Light infantry companies: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```