## Step 1: Define the symbolic representation of the variables
The variables are 'air defense batteries', 'signal platoons', and 'medical platoons', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : air defense batteries
- $x_1$ : signal platoons
- $x_2$ : medical platoons

## 3: Define the objective function in symbolic notation
The objective function to maximize is $2x_0 + 6x_1 + 5x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
1. $15x_0 + 17x_1 \geq 35$ (air defense batteries plus signal platoons must contribute a total fuel demand of at least 35 gallons/day)
2. $x_0 + 12x_1 \leq 196$ (The total combined offensive capability rating from air defense batteries, and signal platoons should be 196 or less)
3. $x_0 + 3x_2 \leq 283$ (The total combined offensive capability rating from air defense batteries plus medical platoons should be 283 at maximum)
4. $x_0 + 12x_1 + 3x_2 \leq 247$ (The total combined offensive capability rating from air defense batteries plus signal platoons plus medical platoons has to be 247 or less)
5. $17x_1 + 5x_2 \leq 140$ (signal platoons plus medical platoons has to have a total fuel demand of at most 140 gal/day)
6. $15x_0 + 17x_1 + 5x_2 \leq 96$ (air defense batteries plus signal platoons plus medical platoons must have a total fuel demand of no more than 96 gal per day)
7. $x_0 \in \mathbb{Z}$ (There cannot be a fractional amount of air defense batteries)
8. $x_1 \in \mathbb{Z}$ (A whole number of signal platoons must be used)
9. $x_2 \in \mathbb{Z}$ (A whole number of medical platoons must be used)

## 5: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x0', 'air defense batteries'), ('x1', 'signal platoons'), ('x2', 'medical platoons')],
    'objective_function': '2*x0 + 6*x1 + 5*x2',
    'constraints': [
        '15*x0 + 17*x1 >= 35',
        'x0 + 12*x1 <= 196',
        'x0 + 3*x2 <= 283',
        'x0 + 12*x1 + 3*x2 <= 247',
        '17*x1 + 5*x2 <= 140',
        '15*x0 + 17*x1 + 5*x2 <= 96',
        'x0 >= 0',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 6: Write the Gurobi code to solve the optimization problem
```python
import gurobipy as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="air_defense_batteries", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="signal_platoons", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="medical_platoons", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(2*x0 + 6*x1 + 5*x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x0 + 17*x1 >= 35, name="fuel_demand_constraint")
m.addConstr(x0 + 12*x1 <= 196, name="offensive_capability_rating_constraint_1")
m.addConstr(x0 + 3*x2 <= 283, name="offensive_capability_rating_constraint_2")
m.addConstr(x0 + 12*x1 + 3*x2 <= 247, name="offensive_capability_rating_constraint_3")
m.addConstr(17*x1 + 5*x2 <= 140, name="fuel_demand_constraint_2")
m.addConstr(15*x0 + 17*x1 + 5*x2 <= 96, name="total_fuel_demand_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Air defense batteries: {x0.varValue}")
    print(f"Signal platoons: {x1.varValue}")
    print(f"Medical platoons: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```