To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each type of unit, formulating the objective function using these variables, and then listing out all constraints in terms of these variables.

Let's denote:
- \(x_1\) as the number of airborne infantry companies,
- \(x_2\) as the number of pathfinder teams,
- \(x_3\) as the number of logistics companies,
- \(x_4\) as the number of water purification units, and
- \(x_5\) as the number of air defense batteries.

The objective function to minimize is: \(5x_1 + 8x_2 + 5x_3 + 9x_4 + 5x_5\).

Constraints are:
1. The total combined offensive capability rating from airborne infantry companies and water purification units should be as much or more than 24: \(1x_1 + 1x_4 \geq 24\).
2. The total combined offensive capability rating from airborne infantry companies plus air defense batteries should be greater than or equal to 31: \(1x_1 + 2x_5 \geq 31\).
3. The total combined offensive capability rating from all units must be at least 31: \(1x_1 + 3x_2 + 1x_3 + 1x_4 + 2x_5 \geq 31\).
4. All variables are restricted to non-negative integers.

Given this, the symbolic representation of the problem is:
```json
{
    'sym_variables': [
        ('x1', 'airborne infantry companies'), 
        ('x2', 'pathfinder teams'), 
        ('x3', 'logistics companies'), 
        ('x4', 'water purification units'), 
        ('x5', 'air defense batteries')
    ], 
    'objective_function': '5*x1 + 8*x2 + 5*x3 + 9*x4 + 5*x5', 
    'constraints': [
        'x1 + x4 >= 24', 
        'x1 + 2*x5 >= 31', 
        'x1 + 3*x2 + x3 + x4 + 2*x5 >= 31'
    ]
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="airborne_infantry_companies")
x2 = m.addVar(vtype=GRB.INTEGER, name="pathfinder_teams")
x3 = m.addVar(vtype=GRB.INTEGER, name="logistics_companies")
x4 = m.addVar(vtype=GRB.INTEGER, name="water_purification_units")
x5 = m.addVar(vtype=GRB.INTEGER, name="air_defense_batteries")

# Objective function
m.setObjective(5*x1 + 8*x2 + 5*x3 + 9*x4 + 5*x5, GRB.MINIMIZE)

# Constraints
m.addConstr(x1 + x4 >= 24, "offensive_capability_1")
m.addConstr(x1 + 2*x5 >= 31, "offensive_capability_2")
m.addConstr(x1 + 3*x2 + x3 + x4 + 2*x5 >= 31, "total_offensive_capability")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Airborne Infantry Companies: {x1.x}")
    print(f"Pathfinder Teams: {x2.x}")
    print(f"Logistics Companies: {x3.x}")
    print(f"Water Purification Units: {x4.x}")
    print(f"Air Defense Batteries: {x5.x}")
else:
    print("No optimal solution found.")
```