## Step 1: Define the symbolic representation of the variables
The variables are: 
- 'airborne infantry companies' 
- 'pathfinder teams' 
- 'logistics companies' 
- 'water purification units' 
- 'air defense batteries'

Let's denote them as $x_1, x_2, x_3, x_4, x_5$ respectively.

## Step 2: Formulate the objective function
The objective function to minimize is: $5x_1 + 8x_2 + 5x_3 + 9x_4 + 5x_5$.

## 3: Define the constraints
- The offensive capability ratings are: $x_1$ has a rating of 1, $x_2$ has a rating of 3, $x_3$ has a rating of 1, $x_4$ has a rating of 1, and $x_5$ has a rating of 2.
- The total combined offensive capability rating from $x_1$ and $x_4$ should be as much or more than 24: $x_1 + x_4 \geq 24$.
- The total combined offensive capability rating from $x_1$ and $x_5$ should be greater than or equal to 31: $x_1 + 2x_5 \geq 31$.
- The total combined offensive capability rating from all variables must be 31 at a minimum: $x_1 + 3x_2 + x_3 + x_4 + 2x_5 \geq 31$.
- All variables must be integers.

## 4: Symbolic Representation
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'
    ]
}
```

## 5: Gurobi Code
Now, let's write the Gurobi code for this problem:
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name='airborne_infantry_companies', obj=5, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='pathfinder_teams', obj=8, vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name='logistics_companies', obj=5, vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name='water_purification_units', obj=9, vtype=gurobi.GRB.INTEGER)
    x5 = model.addVar(name='air_defense_batteries', obj=5, vtype=gurobi.GRB.INTEGER)

    # Add constraints
    model.addConstr(x1 + x4 >= 24, name='offensive_capability_rating_1')
    model.addConstr(x1 + 2*x5 >= 31, name='offensive_capability_rating_2')
    model.addConstr(x1 + 3*x2 + x3 + x4 + 2*x5 >= 31, name='total_offensive_capability_rating')

    # Set the objective function
    model.setObjective(5*x1 + 8*x2 + 5*x3 + 9*x4 + 5*x5, gurobi.GRB.MINIMIZE)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('Airborne Infantry Companies: ', x1.varValue)
        print('Pathfinder Teams: ', x2.varValue)
        print('Logistics Companies: ', x3.varValue)
        print('Water Purification Units: ', x4.varValue)
        print('Air Defense Batteries: ', x5.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```