## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'air defense batteries', 'CBRN platoons', and 'armored companies', which we can denote as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $2x_1^2 + 3x_3^2 + 7x_2$.

## 3: List the constraints in symbolic notation
1. $13.82x_1 \leq 192$
2. $11.71x_1 \leq 111$
3. $12.86x_1 \leq 243$
4. $0.07x_2 \leq 192$
5. $9.6x_2 \leq 111$
6. $28.74x_2 \leq 243$
7. $18.43x_3 \leq 192$
8. $5.43x_3 \leq 111$
9. $20.84x_3 \leq 243$
10. $13.82x_1^2 + 18.43x_3^2 \geq 58$
11. $11.71x_1^2 + 5.43x_3^2 \geq 12$
12. $9.6x_2 + 5.43x_3 \geq 35$
13. $28.74x_2^2 + 20.84x_3^2 \geq 64$
14. $13.82x_1^2 + 0.07x_2^2 \leq 144$
15. $0.07x_2 + 18.43x_3 \leq 65$
16. $13.82x_1^2 + 18.43x_3^2 \leq 119$
17. $13.82x_1 + 0.07x_2 + 18.43x_3 \leq 119$
18. $11.71x_1 + 5.43x_3 \leq 45$
19. $11.71x_1 + 9.6x_2 \leq 77$
20. $11.71x_1^2 + 9.6x_2^2 + 5.43x_3^2 \leq 90$
21. $11.71x_1 + 9.6x_2 + 5.43x_3 \leq 90$
22. $12.86x_1^2 + 28.74x_2^2 \leq 198$
23. $28.74x_2 + 20.84x_3 \leq 240$
24. $12.86x_1 + 28.74x_2 + 20.84x_3 \leq 240$
25. $x_1, x_2, x_3 \geq 0$ and are integers.

## 4: Define the symbolic variables and constraints for the output
```json
{
    'sym_variables': [
        ('x1', 'air defense batteries'), 
        ('x2', 'CBRN platoons'), 
        ('x3', 'armored companies')
    ], 
    'objective_function': '2*x1^2 + 7*x2 + 3*x3^2', 
    'constraints': [
        '13.82*x1 <= 192',
        '11.71*x1 <= 111',
        '12.86*x1 <= 243',
        '0.07*x2 <= 192',
        '9.6*x2 <= 111',
        '28.74*x2 <= 243',
        '18.43*x3 <= 192',
        '5.43*x3 <= 111',
        '20.84*x3 <= 243',
        '13.82*x1^2 + 18.43*x3^2 >= 58',
        '11.71*x1^2 + 5.43*x3^2 >= 12',
        '9.6*x2 + 5.43*x3 >= 35',
        '28.74*x2^2 + 20.84*x3^2 >= 64',
        '13.82*x1^2 + 0.07*x2^2 <= 144',
        '0.07*x2 + 18.43*x3 <= 65',
        '13.82*x1^2 + 18.43*x3^2 <= 119',
        '13.82*x1 + 0.07*x2 + 18.43*x3 <= 119',
        '11.71*x1 + 5.43*x3 <= 45',
        '11.71*x1 + 9.6*x2 <= 77',
        '11.71*x1^2 + 9.6*x2^2 + 5.43*x3^2 <= 90',
        '11.71*x1 + 9.6*x2 + 5.43*x3 <= 90',
        '12.86*x1^2 + 28.74*x2^2 <= 198',
        '28.74*x2 + 20.84*x3 <= 240',
        '12.86*x1 + 28.74*x2 + 20.84*x3 <= 240'
    ]
}
```

## 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name="air_defense_batteries", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="CBRN_platoons", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="armored_companies", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(2*x1**2 + 7*x2 + 3*x3**2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(13.82*x1 <= 192)
m.addConstr(11.71*x1 <= 111)
m.addConstr(12.86*x1 <= 243)
m.addConstr(0.07*x2 <= 192)
m.addConstr(9.6*x2 <= 111)
m.addConstr(28.74*x2 <= 243)
m.addConstr(18.43*x3 <= 192)
m.addConstr(5.43*x3 <= 111)
m.addConstr(20.84*x3 <= 243)
m.addConstr(13.82*x1**2 + 18.43*x3**2 >= 58)
m.addConstr(11.71*x1**2 + 5.43*x3**2 >= 12)
m.addConstr(9.6*x2 + 5.43*x3 >= 35)
m.addConstr(28.74*x2**2 + 20.84*x3**2 >= 64)
m.addConstr(13.82*x1**2 + 0.07*x2**2 <= 144)
m.addConstr(0.07*x2 + 18.43*x3 <= 65)
m.addConstr(13.82*x1**2 + 18.43*x3**2 <= 119)
m.addConstr(13.82*x1 + 0.07*x2 + 18.43*x3 <= 119)
m.addConstr(11.71*x1 + 5.43*x3 <= 45)
m.addConstr(11.71*x1 + 9.6*x2 <= 77)
m.addConstr(11.71*x1**2 + 9.6*x2**2 + 5.43*x3**2 <= 90)
m.addConstr(11.71*x1 + 9.6*x2 + 5.43*x3 <= 90)
m.addConstr(12.86*x1**2 + 28.74*x2**2 <= 198)
m.addConstr(28.74*x2 + 20.84*x3 <= 240)
m.addConstr(12.86*x1 + 28.74*x2 + 20.84*x3 <= 240)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Air defense batteries: ", x1.varValue)
    print("CBRN platoons: ", x2.varValue)
    print("Armored companies: ", x3.varValue)
else:
    print("The model is infeasible")
```