## Step 1: Define the symbolic representation of the variables
The variables are 'airborne infantry companies' and 'engineer platoons', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $2.27x_1 + 4.98x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $10x_1 + 4x_2 \geq 28$ (total logistics footprint minimum)
- $10x_1 + 4x_2 \leq 76$ (logistics footprint upper bound)
- $8x_1 + 10x_2 \geq 34$ (total logistical capacity minimum)
- $8x_1 + 10x_2 \leq 85$ (logistical capacity upper bound)
- $6x_1 + 6x_2 \geq 41$ (total mobility rating minimum)
- $6x_1 + 6x_2 \leq 118$ (mobility rating upper bound)
- $6x_1 - 4x_2 \geq 0$ (specific constraint)
- $10x_1 + 4x_2 \leq 55$ is not valid as per the problem description, instead we have $10x_1 + 4x_2 \geq 28$ and $10x_1 + 4x_2 \leq 76$
- $8x_1 + 10x_2 \leq 69$ (additional upper bound for logistical capacity)
- $6x_1 + 6x_2 \leq 115$ (additional upper bound for mobility rating)
- $x_1$ and $x_2$ must be integers.

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(vtype=gurobi.GRB.INTEGER, name="airborne_infantry_companies")
x2 = model.addVar(vtype=gurobi.GRB.INTEGER, name="engineer_platoons")

# Define the objective function
model.setObjective(2.27 * x1 + 4.98 * x2, gurobi.GRB.MINIMIZE)

# Define the constraints
model.addConstr(10 * x1 + 4 * x2 >= 28, name="logistics_footprint_min")
model.addConstr(10 * x1 + 4 * x2 <= 76, name="logistics_footprint_max")
model.addConstr(8 * x1 + 10 * x2 >= 34, name="logistical_capacity_min")
model.addConstr(8 * x1 + 10 * x2 <= 69, name="logistical_capacity_max")
model.addConstr(6 * x1 + 6 * x2 >= 41, name="mobility_rating_min")
model.addConstr(6 * x1 + 6 * x2 <= 115, name="mobility_rating_max")
model.addConstr(6 * x1 - 4 * x2 >= 0, name="specific_constraint")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Airborne Infantry Companies: ", x1.varValue)
    print("Engineer Platoons: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 5: Symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'airborne infantry companies'), ('x2', 'engineer platoons')],
    'objective_function': '2.27*x1 + 4.98*x2',
    'constraints': [
        '10*x1 + 4*x2 >= 28',
        '10*x1 + 4*x2 <= 76',
        '8*x1 + 10*x2 >= 34',
        '8*x1 + 10*x2 <= 69',
        '6*x1 + 6*x2 >= 41',
        '6*x1 + 6*x2 <= 115',
        '6*x1 - 4*x2 >= 0'
    ]
}
```