## Step 1: Define the symbolic representation of the variables
The variables are 'pathfinder teams', 'artillery batteries', 'CBRN platoons', 'logistics companies' which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $5x_0 + 3x_1 + 5x_2 + 8x_3$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $8x_1 + 15x_3 \geq 45$
- $16x_0 + 10x_2 \geq 43$
- $8x_1 + 10x_2 \geq 49$
- $8x_1 + 10x_2 + 15x_3 \geq 58$
- $16x_0 + 10x_2 + 15x_3 \geq 58$
- $8x_1 + 10x_2 + 15x_3 \geq 41$
- $16x_0 + 10x_2 \geq 41$
- $9x_1 + 6x_2 \geq 62$
- $9x_1 + 13x_3 \geq 66$
- $1x_0 + 13x_3 \geq 36$
- $6x_2 + 13x_3 \geq 74$
- $16x_0 + 15x_3 \leq 123$
- $8x_1 + 15x_3 \leq 161$
- $16x_0 + 8x_1 \leq 215$
- $16x_0 + 8x_1 + 10x_2 + 15x_3 \leq 215$
- $1x_0 + 6x_2 \leq 220$
- $1x_0 + 13x_3 \leq 113$
- $9x_1 + 13x_3 \leq 141$
- $6x_2 + 13x_3 \leq 329$
- $1x_0 + 9x_1 + 6x_2 + 13x_3 \leq 329$

## 4: Represent the problem in JSON format
```json
{
    'sym_variables': [('x0', 'pathfinder teams'), ('x1', 'artillery batteries'), ('x2', 'CBRN platoons'), ('x3', 'logistics companies')],
    'objective_function': '5*x0 + 3*x1 + 5*x2 + 8*x3',
    'constraints': [
        '8*x1 + 15*x3 >= 45',
        '16*x0 + 10*x2 >= 43',
        '8*x1 + 10*x2 >= 49',
        '8*x1 + 10*x2 + 15*x3 >= 58',
        '16*x0 + 10*x2 + 15*x3 >= 58',
        '8*x1 + 10*x2 + 15*x3 >= 41',
        '16*x0 + 10*x2 >= 41',
        '9*x1 + 6*x2 >= 62',
        '9*x1 + 13*x3 >= 66',
        'x0 + 13*x3 >= 36',
        '6*x2 + 13*x3 >= 74',
        '16*x0 + 15*x3 <= 123',
        '8*x1 + 15*x3 <= 161',
        '16*x0 + 8*x1 <= 215',
        '16*x0 + 8*x1 + 10*x2 + 15*x3 <= 215',
        'x0 + 6*x2 <= 220',
        'x0 + 13*x3 <= 113',
        '9*x1 + 13*x3 <= 141',
        '6*x2 + 13*x3 <= 329',
        'x0 + 9*x1 + 6*x2 + 13*x3 <= 329'
    ]
}
```

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

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # pathfinder teams
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # artillery batteries
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # CBRN platoons
    x3 = model.addVar(name="x3", vtype=gurobi.GRB.INTEGER)  # logistics companies

    # Objective function
    model.setObjective(5*x0 + 3*x1 + 5*x2 + 8*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(8*x1 + 15*x3 >= 45)
    model.addConstr(16*x0 + 10*x2 >= 43)
    model.addConstr(8*x1 + 10*x2 >= 49)
    model.addConstr(8*x1 + 10*x2 + 15*x3 >= 58)
    model.addConstr(16*x0 + 10*x2 + 15*x3 >= 58)
    model.addConstr(8*x1 + 10*x2 + 15*x3 >= 41)
    model.addConstr(16*x0 + 10*x2 >= 41)
    model.addConstr(9*x1 + 6*x2 >= 62)
    model.addConstr(9*x1 + 13*x3 >= 66)
    model.addConstr(x0 + 13*x3 >= 36)
    model.addConstr(6*x2 + 13*x3 >= 74)
    model.addConstr(16*x0 + 15*x3 <= 123)
    model.addConstr(8*x1 + 15*x3 <= 161)
    model.addConstr(16*x0 + 8*x1 <= 215)
    model.addConstr(16*x0 + 8*x1 + 10*x2 + 15*x3 <= 215)
    model.addConstr(x0 + 6*x2 <= 220)
    model.addConstr(x0 + 13*x3 <= 113)
    model.addConstr(9*x1 + 13*x3 <= 141)
    model.addConstr(6*x2 + 13*x3 <= 329)
    model.addConstr(x0 + 9*x1 + 6*x2 + 13*x3 <= 329)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Pathfinder teams: ", x0.varValue)
        print("Artillery batteries: ", x1.varValue)
        print("CBRN platoons: ", x2.varValue)
        print("Logistics companies: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```