## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are:
- $x_0$: airborne infantry companies
- $x_1$: light infantry companies
- $x_2$: military intelligence companies
- $x_3$: air defense batteries

The objective function to maximize is: $x_0 + x_1 + 5x_2 + 7x_3$

## Step 2: List the constraints in symbolic notation
Constraints:
1. $17x_0 + 12x_1 + 11x_2 + 5x_3 \geq 28$
2. $13x_2 + 8x_3 \geq 14$
3. $3x_0 + 13x_2 \geq 26$
4. $2x_1 + 13x_2 \geq 24$
5. $3x_0 + 2x_1 + 13x_2 \geq 17$
6. $3x_0 + 13x_2 + 8x_3 \geq 17$
7. $2x_1 + 13x_2 + 8x_3 \geq 17$
8. $3x_0 + 2x_1 + 13x_2 \geq 25$
9. $3x_0 + 13x_2 + 8x_3 \geq 25$
10. $2x_1 + 13x_2 + 8x_3 \geq 26$
11. $3x_0 + 2x_1 + 13x_2 \geq 26$
12. $3x_0 + 13x_2 + 8x_3 \geq 26$
13. $2x_1 + 13x_2 + 8x_3 \geq 26$
14. $17x_0 + 4x_3 \geq 5$
15. $17x_0 + 9x_1 \geq 14$
16. $7x_2 + 4x_3 \geq 6$
17. $17x_0 + 5x_3 \leq 59$
18. $12x_1 + 11x_2 \leq 64$
19. $12x_1 + 5x_3 \leq 103$
20. $17x_0 + 12x_1 + 11x_2 \leq 51$
21. $17x_0 + 12x_1 + 11x_2 + 5x_3 \leq 51$
22. $3x_0 + 2x_1 \leq 64$
23. $13x_2 + 8x_3 \leq 93$
24. $3x_0 + 2x_1 + 13x_2 + 8x_3 \leq 93$
25. $9x_1 + 7x_2 \leq 28$
26. $9x_1 + 4x_3 \leq 27$
27. $17x_0 + 9x_1 \leq 34$
28. $17x_0 + 4x_3 \leq 34$
29. $17x_0 + 9x_1 + 7x_2 \leq 28$
30. $9x_1 + 7x_2 + 4x_3 \leq 26$
31. $17x_0 + 9x_1 + 4x_3 \leq 28$
32. $17x_0 + 9x_1 + 7x_2 + 4x_3 \leq 28$

## Step 3: Define the symbolic representation
```json
{
    'sym_variables': [
        ('x0', 'airborne infantry companies'),
        ('x1', 'light infantry companies'),
        ('x2', 'military intelligence companies'),
        ('x3', 'air defense batteries')
    ],
    'objective_function': 'x0 + x1 + 5*x2 + 7*x3',
    'constraints': [
        '17*x0 + 12*x1 + 11*x2 + 5*x3 >= 28',
        '13*x2 + 8*x3 >= 14',
        '3*x0 + 13*x2 >= 26',
        '2*x1 + 13*x2 >= 24',
        '3*x0 + 2*x1 + 13*x2 >= 17',
        '3*x0 + 13*x2 + 8*x3 >= 17',
        '2*x1 + 13*x2 + 8*x3 >= 17',
        '3*x0 + 2*x1 + 13*x2 >= 25',
        '3*x0 + 13*x2 + 8*x3 >= 25',
        '2*x1 + 13*x2 + 8*x3 >= 26',
        '3*x0 + 2*x1 + 13*x2 >= 26',
        '3*x0 + 13*x2 + 8*x3 >= 26',
        '2*x1 + 13*x2 + 8*x3 >= 26',
        '17*x0 + 4*x3 >= 5',
        '17*x0 + 9*x1 >= 14',
        '7*x2 + 4*x3 >= 6',
        '17*x0 + 5*x3 <= 59',
        '12*x1 + 11*x2 <= 64',
        '12*x1 + 5*x3 <= 103',
        '17*x0 + 12*x1 + 11*x2 <= 51',
        '17*x0 + 12*x1 + 11*x2 + 5*x3 <= 51',
        '3*x0 + 2*x1 <= 64',
        '13*x2 + 8*x3 <= 93',
        '3*x0 + 2*x1 + 13*x2 + 8*x3 <= 93',
        '9*x1 + 7*x2 <= 28',
        '9*x1 + 4*x3 <= 27',
        '17*x0 + 9*x1 <= 34',
        '17*x0 + 4*x3 <= 34',
        '17*x0 + 9*x1 + 7*x2 <= 28',
        '9*x1 + 7*x2 + 4*x3 <= 26',
        '17*x0 + 9*x1 + 4*x3 <= 28',
        '17*x0 + 9*x1 + 7*x2 + 4*x3 <= 28'
    ]
}
```

## Step 4: Implement the optimization problem using Gurobi
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="airborne_infantry_companies", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="light_infantry_companies", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="military_intelligence_companies", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="air_defense_batteries", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(x0 + x1 + 5*x2 + 7*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(17*x0 + 12*x1 + 11*x2 + 5*x3 >= 28)
    model.addConstr(13*x2 + 8*x3 >= 14)
    model.addConstr(3*x0 + 13*x2 >= 26)
    model.addConstr(2*x1 + 13*x2 >= 24)
    model.addConstr(3*x0 + 2*x1 + 13*x2 >= 17)
    model.addConstr(3*x0 + 13*x2 + 8*x3 >= 17)
    model.addConstr(2*x1 + 13*x2 + 8*x3 >= 17)
    model.addConstr(3*x0 + 2*x1 + 13*x2 >= 25)
    model.addConstr(3*x0 + 13*x2 + 8*x3 >= 25)
    model.addConstr(2*x1 + 13*x2 + 8*x3 >= 26)
    model.addConstr(3*x0 + 2*x1 + 13*x2 >= 26)
    model.addConstr(3*x0 + 13*x2 + 8*x3 >= 26)
    model.addConstr(2*x1 + 13*x2 + 8*x3 >= 26)
    model.addConstr(17*x0 + 4*x3 >= 5)
    model.addConstr(17*x0 + 9*x1 >= 14)
    model.addConstr(7*x2 + 4*x3 >= 6)
    model.addConstr(17*x0 + 5*x3 <= 59)
    model.addConstr(12*x1 + 11*x2 <= 64)
    model.addConstr(12*x1 + 5*x3 <= 103)
    model.addConstr(17*x0 + 12*x1 + 11*x2 <= 51)
    model.addConstr(17*x0 + 12*x1 + 11*x2 + 5*x3 <= 51)
    model.addConstr(3*x0 + 2*x1 <= 64)
    model.addConstr(13*x2 + 8*x3 <= 93)
    model.addConstr(3*x0 + 2*x1 + 13*x2 + 8*x3 <= 93)
    model.addConstr(9*x1 + 7*x2 <= 28)
    model.addConstr(9*x1 + 4*x3 <= 27)
    model.addConstr(17*x0 + 9*x1 <= 34)
    model.addConstr(17*x0 + 4*x3 <= 34)
    model.addConstr(17*x0 + 9*x1 + 7*x2 <= 28)
    model.addConstr(9*x1 + 7*x2 + 4*x3 <= 26)
    model.addConstr(17*x0 + 9*x1 + 4*x3 <= 28)
    model.addConstr(17*x0 + 9*x1 + 7*x2 + 4*x3 <= 28)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Airborne Infantry Companies: ", x0.varValue)
        print("Light Infantry Companies: ", x1.varValue)
        print("Military Intelligence Companies: ", x2.varValue)
        print("Air Defense Batteries: ", x3.varValue)
    else:
        print("No optimal solution found")

optimize_problem()
```