## Step 1: Define the symbolic representation of the variables
The variables are ['medical platoons', 'signal platoons', 'water purification units', 'mechanized infantry companies', 'armored companies']. Let's denote them as $x_1, x_2, x_3, x_4, x_5$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $6 \times \text{medical platoons} + 2 \times \text{signal platoons} + 9 \times \text{water purification units} + 1 \times \text{mechanized infantry companies} + 1 \times \text{armored companies}$. In symbolic terms, this is $6x_1 + 2x_2 + 9x_3 + x_4 + x_5$.

## 3: Define the constraints in symbolic notation
1. $\text{medical platoons} \times 5 \leq 92$ => $5x_1 \leq 92$
2. $\text{signal platoons} \times 5 \leq 92$ => $5x_2 \leq 92$
3. $\text{water purification units} \times 1 \leq 92$ => $x_3 \leq 92$
4. $\text{mechanized infantry companies} \times 2 \leq 92$ => $2x_4 \leq 92$
5. $\text{armored companies} \times 3 \leq 92$ => $3x_5 \leq 92$
6. $5x_1 + 5x_2 \geq 6$
7. $5x_1 + 2x_4 \geq 18$
8. $2x_4 + 3x_5 \geq 17$
9. $5x_1 + 5x_2 + 2x_4 \geq 9$
10. $5x_2 + 2x_4 + 3x_5 \geq 9$
11. $5x_1 + 5x_2 + 2x_4 \geq 14$
12. $5x_2 + 2x_4 + 3x_5 \geq 14$
13. $-10x_2 + 7x_5 \geq 0$
14. $5x_2 + 3x_5 \leq 64$
15. $5x_2 + 2x_4 \leq 46$
16. $5x_2 + x_3 + 3x_5 \leq 30$
17. $x_3 + 2x_4 + 3x_5 \leq 58$
18. $5x_1 + 2x_4 + 3x_5 \leq 41$
19. $5x_1 + x_3 + 2x_4 \leq 45$
20. $5x_1 + 5x_2 + x_3 + 2x_4 + 3x_5 \leq 45$

## 4: Express the problem in JSON format
```json
{
    'sym_variables': [
        ('x1', 'medical platoons'),
        ('x2', 'signal platoons'),
        ('x3', 'water purification units'),
        ('x4', 'mechanized infantry companies'),
        ('x5', 'armored companies')
    ],
    'objective_function': '6*x1 + 2*x2 + 9*x3 + x4 + x5',
    'constraints': [
        '5*x1 <= 92',
        '5*x2 <= 92',
        'x3 <= 92',
        '2*x4 <= 92',
        '3*x5 <= 92',
        '5*x1 + 5*x2 >= 6',
        '5*x1 + 2*x4 >= 18',
        '2*x4 + 3*x5 >= 17',
        '5*x1 + 5*x2 + 2*x4 >= 9',
        '5*x2 + 2*x4 + 3*x5 >= 9',
        '5*x1 + 5*x2 + 2*x4 >= 14',
        '5*x2 + 2*x4 + 3*x5 >= 14',
        '-10*x2 + 7*x5 >= 0',
        '5*x2 + 3*x5 <= 64',
        '5*x2 + 2*x4 <= 46',
        '5*x2 + x3 + 3*x5 <= 30',
        'x3 + 2*x4 + 3*x5 <= 58',
        '5*x1 + 2*x4 + 3*x5 <= 41',
        '5*x1 + x3 + 2*x4 <= 45',
        '5*x1 + 5*x2 + x3 + 2*x4 + 3*x5 <= 45'
    ]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name="medical_platoons", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="signal_platoons", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="water_purification_units", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="mechanized_infantry_companies", vtype=gurobi.GRB.INTEGER)
    x5 = model.addVar(name="armored_companies", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(6 * x1 + 2 * x2 + 9 * x3 + x4 + x5, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(5 * x1 <= 92)
    model.addConstr(5 * x2 <= 92)
    model.addConstr(x3 <= 92)
    model.addConstr(2 * x4 <= 92)
    model.addConstr(3 * x5 <= 92)
    model.addConstr(5 * x1 + 5 * x2 >= 6)
    model.addConstr(5 * x1 + 2 * x4 >= 18)
    model.addConstr(2 * x4 + 3 * x5 >= 17)
    model.addConstr(5 * x1 + 5 * x2 + 2 * x4 >= 9)
    model.addConstr(5 * x2 + 2 * x4 + 3 * x5 >= 9)
    model.addConstr(5 * x1 + 5 * x2 + 2 * x4 >= 14)
    model.addConstr(5 * x2 + 2 * x4 + 3 * x5 >= 14)
    model.addConstr(-10 * x2 + 7 * x5 >= 0)
    model.addConstr(5 * x2 + 3 * x5 <= 64)
    model.addConstr(5 * x2 + 2 * x4 <= 46)
    model.addConstr(5 * x2 + x3 + 3 * x5 <= 30)
    model.addConstr(x3 + 2 * x4 + 3 * x5 <= 58)
    model.addConstr(5 * x1 + 2 * x4 + 3 * x5 <= 41)
    model.addConstr(5 * x1 + x3 + 2 * x4 <= 45)
    model.addConstr(5 * x1 + 5 * x2 + x3 + 2 * x4 + 3 * x5 <= 45)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Medical platoons: ", x1.varValue)
        print("Signal platoons: ", x2.varValue)
        print("Water purification units: ", x3.varValue)
        print("Mechanized infantry companies: ", x4.varValue)
        print("Armored companies: ", x5.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```