## Step 1: Define the symbolic representation of the variables
The variables are: 
- 'military intelligence companies' 
- 'water purification units' 
- 'armored companies' 
- 'light infantry companies'

Let's denote them as:
- $x_0$ : 'military intelligence companies'
- $x_1$ : 'water purification units'
- $x_2$ : 'armored companies'
- $x_3$ : 'light infantry companies'

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is: $7x_0 + 3x_1 + 9x_2 + 3x_3$

## Step 3: Define the constraints in symbolic notation
Given:
- $r_0$ : defensive capability rating
- $r_1$ : logistics footprint

Constraints:
1. $2x_0 + 6x_1 + 6x_2 + 4x_3 \geq 12$
2. $4x_0 + 4x_1 \geq 5$
3. $4x_0 + 4x_1 + 7x_3 \geq 9$
4. $6x_2 + 4x_3 \leq 35$
5. $2x_0 + 6x_1 \leq 43$
6. $2x_0 + 4x_3 \leq 31$
7. $2x_0 + 6x_2 \leq 47$
8. $6x_1 + 6x_2 \leq 37$
9. $6x_1 + 6x_2 + 4x_3 \leq 39$
10. $2x_0 + 6x_1 + 6x_2 + 4x_3 \leq 39$
11. $x_2 + 7x_3 \leq 30$
12. $4x_0 + 4x_1 \leq 36$
13. $4x_1 + 7x_3 \leq 30$
14. $4x_1 + x_2 \leq 26$
15. $4x_0 + x_2 \leq 18$
16. $4x_0 + 4x_1 + x_2 + 7x_3 \leq 18$

## 4: Formulate the problem in Gurobi
We will use Gurobi to solve this linear programming problem.

```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="military_intelligence_companies", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="water_purification_units", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="armored_companies", vtype=gp.GRB.INTEGER)
x3 = m.addVar(name="light_infantry_companies", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(7*x0 + 3*x1 + 9*x2 + 3*x3, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x0 + 6*x1 + 6*x2 + 4*x3 >= 12)
m.addConstr(4*x0 + 4*x1 >= 5)
m.addConstr(4*x0 + 4*x1 + 7*x3 >= 9)
m.addConstr(6*x2 + 4*x3 <= 35)
m.addConstr(2*x0 + 6*x1 <= 43)
m.addConstr(2*x0 + 4*x3 <= 31)
m.addConstr(2*x0 + 6*x2 <= 47)
m.addConstr(6*x1 + 6*x2 <= 37)
m.addConstr(6*x1 + 6*x2 + 4*x3 <= 39)
m.addConstr(2*x0 + 6*x1 + 6*x2 + 4*x3 <= 39)
m.addConstr(x2 + 7*x3 <= 30)
m.addConstr(4*x0 + 4*x1 <= 36)
m.addConstr(4*x1 + 7*x3 <= 30)
m.addConstr(4*x1 + x2 <= 26)
m.addConstr(4*x0 + x2 <= 18)
m.addConstr(4*x0 + 4*x1 + x2 + 7*x3 <= 18)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("military intelligence companies: ", x0.varValue)
    print("water purification units: ", x1.varValue)
    print("armored companies: ", x2.varValue)
    print("light infantry companies: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 5: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [
        ('x0', 'military intelligence companies'),
        ('x1', 'water purification units'),
        ('x2', 'armored companies'),
        ('x3', 'light infantry companies')
    ],
    'objective_function': '7*x0 + 3*x1 + 9*x2 + 3*x3',
    'constraints': [
        '2*x0 + 6*x1 + 6*x2 + 4*x3 >= 12',
        '4*x0 + 4*x1 >= 5',
        '4*x0 + 4*x1 + 7*x3 >= 9',
        '6*x2 + 4*x3 <= 35',
        '2*x0 + 6*x1 <= 43',
        '2*x0 + 4*x3 <= 31',
        '2*x0 + 6*x2 <= 47',
        '6*x1 + 6*x2 <= 37',
        '6*x1 + 6*x2 + 4*x3 <= 39',
        '2*x0 + 6*x1 + 6*x2 + 4*x3 <= 39',
        'x2 + 7*x3 <= 30',
        '4*x0 + 4*x1 <= 36',
        '4*x1 + 7*x3 <= 30',
        '4*x1 + x2 <= 26',
        '4*x0 + x2 <= 18',
        '4*x0 + 4*x1 + x2 + 7*x3 <= 18'
    ]
}
```