## Step 1: Define the symbolic representation of the problem

First, let's define the symbolic representation of the problem. We have four variables: 
- $x_0$ for reconnaissance troops
- $x_1$ for airborne infantry companies
- $x_2$ for signal platoons
- $x_3$ for transportation companies

The objective function to maximize is: $5x_0 + 2x_1 + 4x_2 + 8x_3$

## Step 2: List all the constraints

Now, let's list all the constraints:
1. $4x_0 + 2x_1 \geq 11$
2. $4x_0 + 2x_3 \geq 7$
3. $2x_1 + 2x_3 \geq 18$
4. $2x_1 + 5x_2 \geq 7$
5. $4x_0 + x_3 \geq 10$
6. $5x_1 + 4x_2 \geq 7$
7. $4x_0 + 5x_1 + 4x_2 \geq 6$
8. $4x_0 + 4x_2 + x_3 \geq 6$
9. $5x_1 + 4x_2 + x_3 \geq 6$
10. $4x_0 + 5x_1 + x_3 \geq 6$
11. $4x_0 + 4x_2 + x_3 \geq 6$
12. $5x_1 + 4x_2 + x_3 \geq 6$
13. $4x_0 + 5x_1 + x_3 \geq 6$
14. $4x_0 + 4x_2 + x_3 \geq 7$
15. $5x_1 + 4x_2 + x_3 \geq 7$
16. $4x_0 + 5x_1 + x_3 \geq 7$
17. $4x_0 + 5x_1 + 4x_2 \geq 5$
18. $4x_0 + 4x_2 + x_3 \geq 5$
19. $5x_1 + 4x_2 + x_3 \geq 5$
20. $4x_0 + 5x_1 + x_3 \geq 5$
21. $2x_1 + 2x_3 \leq 27$
22. $4x_0 + 5x_2 \leq 74$
23. $4x_0 + 2x_3 \leq 77$
24. $5x_2 + 2x_3 \leq 61$
25. $4x_0 + 2x_1 + 5x_2 + 2x_3 \leq 61$
26. $4x_0 + x_3 \leq 24$
27. $4x_2 + x_3 \leq 19$
28. $4x_0 + 5x_1 + 4x_2 + x_3 \leq 19$

## Step 3: Define the symbolic variables and objective function

The symbolic variables are:
- $x_0$ for reconnaissance troops
- $x_1$ for airborne infantry companies
- $x_2$ for signal platoons
- $x_3$ for transportation companies

The objective function is: $5x_0 + 2x_1 + 4x_2 + 8x_3$

## 4: Write down the problem in JSON format

```json
{
    'sym_variables': [
        ('x0', 'reconnaissance troops'), 
        ('x1', 'airborne infantry companies'), 
        ('x2', 'signal platoons'), 
        ('x3', 'transportation companies')
    ], 
    'objective_function': '5*x0 + 2*x1 + 4*x2 + 8*x3', 
    'constraints': [
        '4*x0 + 2*x1 >= 11',
        '4*x0 + 2*x3 >= 7',
        '2*x1 + 2*x3 >= 18',
        '2*x1 + 5*x2 >= 7',
        '4*x0 + x3 >= 10',
        '5*x1 + 4*x2 >= 7',
        '4*x0 + 5*x1 + 4*x2 >= 6',
        '4*x0 + 4*x2 + x3 >= 6',
        '5*x1 + 4*x2 + x3 >= 6',
        '4*x0 + 5*x1 + x3 >= 6',
        '4*x0 + 4*x2 + x3 >= 6',
        '5*x1 + 4*x2 + x3 >= 6',
        '4*x0 + 5*x1 + x3 >= 6',
        '4*x0 + 4*x2 + x3 >= 7',
        '5*x1 + 4*x2 + x3 >= 7',
        '4*x0 + 5*x1 + x3 >= 7',
        '4*x0 + 5*x1 + 4*x2 >= 5',
        '4*x0 + 4*x2 + x3 >= 5',
        '5*x1 + 4*x2 + x3 >= 5',
        '4*x0 + 5*x1 + x3 >= 5',
        '2*x1 + 2*x3 <= 27',
        '4*x0 + 5*x2 <= 74',
        '4*x0 + 2*x3 <= 77',
        '5*x2 + 2*x3 <= 61',
        '4*x0 + 2*x1 + 5*x2 + 2*x3 <= 61',
        '4*x0 + x3 <= 24',
        '4*x2 + x3 <= 19',
        '4*x0 + 5*x1 + 4*x2 + x3 <= 19'
    ]
}
```

## 5: Implement the problem using Gurobi

```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="reconnaissance_troops", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="airborne_infantry_companies", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="signal_platoons", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="transportation_companies", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(5 * x0 + 2 * x1 + 4 * x2 + 8 * x3, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(4 * x0 + 2 * x1 >= 11)
m.addConstr(4 * x0 + 2 * x3 >= 7)
m.addConstr(2 * x1 + 2 * x3 >= 18)
m.addConstr(2 * x1 + 5 * x2 >= 7)
m.addConstr(4 * x0 + x3 >= 10)
m.addConstr(5 * x1 + 4 * x2 >= 7)
m.addConstr(4 * x0 + 5 * x1 + 4 * x2 >= 6)
m.addConstr(4 * x0 + 4 * x2 + x3 >= 6)
m.addConstr(5 * x1 + 4 * x2 + x3 >= 6)
m.addConstr(4 * x0 + 5 * x1 + x3 >= 6)
m.addConstr(4 * x0 + 4 * x2 + x3 >= 6)
m.addConstr(5 * x1 + 4 * x2 + x3 >= 6)
m.addConstr(4 * x0 + 5 * x1 + x3 >= 6)
m.addConstr(4 * x0 + 4 * x2 + x3 >= 7)
m.addConstr(5 * x1 + 4 * x2 + x3 >= 7)
m.addConstr(4 * x0 + 5 * x1 + x3 >= 7)
m.addConstr(4 * x0 + 5 * x1 + 4 * x2 >= 5)
m.addConstr(4 * x0 + 4 * x2 + x3 >= 5)
m.addConstr(5 * x1 + 4 * x2 + x3 >= 5)
m.addConstr(4 * x0 + 5 * x1 + x3 >= 5)
m.addConstr(2 * x1 + 2 * x3 <= 27)
m.addConstr(4 * x0 + 5 * x2 <= 74)
m.addConstr(4 * x0 + 2 * x3 <= 77)
m.addConstr(5 * x2 + 2 * x3 <= 61)
m.addConstr(4 * x0 + 2 * x1 + 5 * x2 + 2 * x3 <= 61)
m.addConstr(4 * x0 + x3 <= 24)
m.addConstr(4 * x2 + x3 <= 19)
m.addConstr(4 * x0 + 5 * x1 + 4 * x2 + x3 <= 19)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Reconnaissance troops: ", x0.varValue)
    print("Airborne infantry companies: ", x1.varValue)
    print("Signal platoons: ", x2.varValue)
    print("Transportation companies: ", x3.varValue)
else:
    print("The model is infeasible")
```