To solve this optimization problem, we'll use Gurobi, a popular Python library for mathematical optimization. The goal is to maximize the objective function given, subject to various constraints related to logistics footprints of different military units.

The variables in our problem are:
- `x0`: Number of airborne infantry companies
- `x1`: Number of reconnaissance troops
- `x2`: Number of medical platoons
- `x3`: Number of military intelligence companies

Each type of unit has a logistics footprint associated with it, and there are constraints on the total or combined logistics footprints of various combinations of these units.

Here's how we can translate the given problem into Gurobi code:

```python
from gurobipy import *

# Create a model
m = Model("Military_Unit_Optimization")

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="airborne_infantry_companies")
x1 = m.addVar(vtype=GRB.INTEGER, name="reconnaissance_troops")
x2 = m.addVar(vtype=GRB.INTEGER, name="medical_platoons")
x3 = m.addVar(vtype=GRB.INTEGER, name="military_intelligence_companies")

# Define the objective function
m.setObjective(8.45*x0 + 6.05*x1 + 1.68*x2 + 9.56*x3, GRB.MAXIMIZE)

# Add constraints
m.addConstr(4.55*x0 + 1.03*x2 >= 19, name="logistics_footprint_airborne_medical_min")
m.addConstr(9.92*x1 + 8.91*x3 >= 14, name="logistics_footprint_reconnaissance_intelligence_min")
m.addConstr(9.92*x1 + 1.03*x2 >= 29, name="logistics_footprint_reconnaissance_medical_min")
m.addConstr(4.55*x0 + 8.91*x3 >= 22, name="logistics_footprint_airborne_intelligence_min")
m.addConstr(1.03*x2 + 8.91*x3 >= 25, name="logistics_footprint_medical_intelligence_min")
m.addConstr(9.92*x1 + 1.03*x2 + 8.91*x3 >= 32, name="logistics_footprint_reconnaissance_medical_intelligence_min")
m.addConstr(9.92*x1 + 1.03*x2 <= 71, name="logistics_footprint_reconnaissance_medical_max")
m.addConstr(4.55*x0 + 8.91*x3 <= 37, name="logistics_footprint_airborne_intelligence_max")
m.addConstr(1.03*x2 + 8.91*x3 <= 129, name="logistics_footprint_medical_intelligence_max")
m.addConstr(4.55*x0 + 1.03*x2 + 8.91*x3 <= 68, name="logistics_footprint_airborne_medical_intelligence_max")
m.addConstr(4.55*x0 + 9.92*x1 + 1.03*x2 + 8.91*x3 <= 135, name="total_logistics_footprint_max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Airborne Infantry Companies: {x0.x}")
    print(f"Reconnaissance Troops: {x1.x}")
    print(f"Medical Platoons: {x2.x}")
    print(f"Military Intelligence Companies: {x3.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```