To formulate the given optimization problem in Gurobi, we first need to identify the decision variables, objective function, and constraints. The decision variables are the quantities of signal platoons and light infantry companies to be determined.

### Decision Variables:
- `x0`: Quantity of signal platoons
- `x1`: Quantity of light infantry companies

### Objective Function:
The objective is to maximize the value of 4 times the quantity of signal platoons added to 4 times the quantity of light infantry companies. This can be represented as: Maximize `4*x0 + 4*x1`

### Constraints:
Based on the problem description, we have several constraints related to fuel demand, fun factor, mobility rating, deployment weight, logistics footprint, and additional linear constraints.

1. **Fuel Demand**: At least 78 gallons/day and at most 112 gallons/day.
   - `4*x0 + 12*x1 >= 78`
   - `4*x0 + 12*x1 <= 112`

2. **Fun Factor**: At least 41 and at most 126.
   - `5*x0 + 9*x1 >= 41`
   - `5*x0 + 9*x1 <= 126`

3. **Mobility Rating**: At least 33 and at most 62.
   - `13*x0 + 2*x1 >= 33`
   - `13*x0 + 2*x1 <= 62`

4. **Deployment Weight**: At least 17 metric tons and at most 48 metric tons.
   - `17*x0 + 8*x1 >= 17`
   - `17*x0 + 8*x1 <= 48`

5. **Logistics Footprint**: At least 17 logistics units and at most 25 logistics units.
   - `12*x0 + 14*x1 >= 17`
   - `12*x0 + 14*x1 <= 25`

6. **Additional Linear Constraint**:
   - `-x0 + 9*x1 >= 0`

7. **Integer Constraints**: Both `x0` and `x1` must be integers.

Here's how we can represent this problem in Gurobi using Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Model")

# Decision Variables
x0 = m.addVar(vtype=GRB.INTEGER, name="Signal_Platons")
x1 = m.addVar(vtype=GRB.INTEGER, name="Light_Infantry_Companies")

# Objective Function: Maximize 4*x0 + 4*x1
m.setObjective(4*x0 + 4*x1, GRB.MAXIMIZE)

# Constraints
m.addConstr(4*x0 + 12*x1 >= 78, "Fuel_Demand_Min")
m.addConstr(4*x0 + 12*x1 <= 112, "Fuel_Demand_Max")

m.addConstr(5*x0 + 9*x1 >= 41, "Fun_Factor_Min")
m.addConstr(5*x0 + 9*x1 <= 126, "Fun_Factor_Max")

m.addConstr(13*x0 + 2*x1 >= 33, "Mobility_Rating_Min")
m.addConstr(13*x0 + 2*x1 <= 62, "Mobility_Rating_Max")

m.addConstr(17*x0 + 8*x1 >= 17, "Deployment_Weight_Min")
m.addConstr(17*x0 + 8*x1 <= 48, "Deployment_Weight_Max")

m.addConstr(12*x0 + 14*x1 >= 17, "Logistics_Footprint_Min")
m.addConstr(12*x0 + 14*x1 <= 25, "Logistics_Footprint_Max")

m.addConstr(-x0 + 9*x1 >= 0, "Additional_Constraint")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Signal Platoons: {x0.x}")
    print(f"Light Infantry Companies: {x1.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```