## Step 1: Define the symbolic representation of the variables
The variables are 'reconnaissance troops' and 'pathfinder teams', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $5x_1 + 7x_2$.

## Step 3: Convert the constraints into a symbolic representation
The constraints are:
1. $13x_1 + 20x_2 \geq 45$ (total fuel demand)
2. $13x_1 + 13x_2 \geq 45$ (total logistical capacity)
3. $19x_1 + 15x_2 \geq 41$ (minimum logistics footprint)
4. $x_1 - 7x_2 \geq 0$ (relationship between troops and teams)
5. $13x_1 + 20x_2 \leq 58$ (maximum total fuel demand)
6. $13x_1 + 13x_2 \leq 94$ (maximum total logistical capacity)
7. $19x_1 + 15x_2 \leq 77$ (maximum logistics footprint)
8. $x_1, x_2 \geq 0$ and are integers (nonfractional number of troops and teams)

## 4: Define the problem in JSON format
```json
{
    'sym_variables': [('x1', 'reconnaissance troops'), ('x2', 'pathfinder teams')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '13*x1 + 20*x2 >= 45',
        '13*x1 + 13*x2 >= 45',
        '19*x1 + 15*x2 >= 41',
        'x1 - 7*x2 >= 0',
        '13*x1 + 20*x2 <= 58',
        '13*x1 + 13*x2 <= 94',
        '19*x1 + 15*x2 <= 77',
        'x1, x2 >= 0 and are integers'
    ]
}
```

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

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

# Define the variables
x1 = model.addVar(name='reconnaissance_troops', vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name='pathfinder_teams', vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(5 * x1 + 7 * x2, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(13 * x1 + 20 * x2 >= 45, name='fuel_demand_min')
model.addConstr(13 * x1 + 13 * x2 >= 45, name='logistical_capacity_min')
model.addConstr(19 * x1 + 15 * x2 >= 41, name='logistics_footprint_min')
model.addConstr(x1 - 7 * x2 >= 0, name='troops_to_teams_ratio')
model.addConstr(13 * x1 + 20 * x2 <= 58, name='fuel_demand_max')
model.addConstr(13 * x1 + 13 * x2 <= 94, name='logistical_capacity_max')
model.addConstr(19 * x1 + 15 * x2 <= 77, name='logistics_footprint_max')

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', model.objVal)
    print('Reconnaissance troops: ', x1.varValue)
    print('Pathfinder teams: ', x2.varValue)
else:
    print('The problem is infeasible')
```