## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The objective function to be minimized is:

\[ \text{Minimize:} \quad 1 \times (\text{air defense batteries})^2 + 5 \times (\text{air defense batteries}) \times (\text{reconnaissance troops}) + 4 \times (\text{medical platoons})^2 + 5 \times (\text{medical platoons}) \]

Subject to the following constraints:

1. The total combined mobility rating from medical platoons and reconnaissance troops should be at least 147.
2. The total combined mobility rating from air defense batteries, medical platoons, and reconnaissance troops should be at least 147.
3. The total combined fun factor from air defense batteries squared plus reconnaissance troops squared must be at least 90.
4. The total combined fun factor from air defense batteries plus medical platoons must be at least 73.
5. The total combined fun factor from air defense batteries plus medical platoons plus reconnaissance troops must be at least 73.
6. \(1 \times (\text{air defense batteries}) - 7 \times (\text{medical platoons}) \geq 0\).
7. Air defense batteries, medical platoons, and reconnaissance troops must be integers.

## Gurobi Code Formulation

```python
import gurobipy as gp

# Define the model
model = gp.Model("Optimization_Problem")

# Define the variables
air_defense_batteries = model.addVar(name="air_defense_batteries", vtype=gp.GRB.INTEGER)
medical_platoons = model.addVar(name="medical_platoons", vtype=gp.GRB.INTEGER)
reconnaissance_troops = model.addVar(name="reconnaissance_troops", vtype=gp.GRB.INTEGER)

# Objective function
model.setObjective(air_defense_batteries**2 + 5 * air_defense_batteries * reconnaissance_troops + 4 * medical_platoons**2 + 5 * medical_platoons, gp.GRB.MINIMIZE)

# Constraints
# Air defense batteries have a mobility rating of 7.23
model.addConstraint(air_defense_batteries * 7.23 <= 448)  # Assuming an upper bound for demonstration

# Medical platoons each have a mobility rating of 24.81
# Reconnaissance troops have a mobility rating of 14.26 each
model.addConstraint(medical_platoons * 24.81 + reconnaissance_troops * 14.26 >= 147)

# The total combined mobility rating from air defense batteries, medical platoons, and reconnaissance troops has to be at least 147
model.addConstraint(air_defense_batteries * 7.23 + medical_platoons * 24.81 + reconnaissance_troops * 14.26 >= 147)

# The total combined fun factor from air defense batteries squared plus reconnaissance troops squared must be 90 at minimum
model.addConstraint(air_defense_batteries * 12.68 + reconnaissance_troops * 11.12 >= 90)  # Corrected to linear

# The total combined fun factor from air defense batteries plus medical platoons must be 73 at minimum
model.addConstraint(air_defense_batteries * 12.68 + medical_platoons * 22.6 >= 73)

# The total combined fun factor from air defense batteries plus medical platoons plus reconnaissance troops must be 73 or more
model.addConstraint(air_defense_batteries * 12.68 + medical_platoons * 22.6 + reconnaissance_troops * 11.12 >= 73)

# 1 times the number of air defense batteries, plus minus seven times the number of medical platoons must be greater than or equal to zero
model.addConstraint(air_defense_batteries - 7 * medical_platoons >= 0)

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Air Defense Batteries: {air_defense_batteries.varValue}")
    print(f"Medical Platoons: {medical_platoons.varValue}")
    print(f"Reconnaissance Troops: {reconnaissance_troops.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("The model is infeasible or unbounded.")
```