To tackle this problem, let's first break down the natural language description into a symbolic representation that can be used to formulate the optimization problem.

### Symbolic Representation

Given variables:
- `x0`: reconnaissance troops
- `x1`: engineer platoons

Objective Function: Minimize `4*x0 + 5*x1`

Constraints:

1. Deployment weight constraint for reconnaissance troops: `16*x0`
2. Fun factor of reconnaissance troops: `2*x0`
3. Deployment weight of engineer platoons: `14*x1`
4. Fun factor of engineer platoons: `1*x1`
5. Minimum deployment weight: `16*x0 + 14*x1 >= 81`
6. Minimum fun factor requirement: `2*x0 + 1*x1 >= 58`
7. Linear constraint: `-2*x0 + 7*x1 >= 0`
8. Maximum deployment weight: `16*x0 + 14*x1 <= 177` (corrected from the original problem statement to match the provided resource attribute)
9. Maximum fun factor: `2*x0 + 1*x1 <= 116`
10. Integer constraints for both variables: `x0` and `x1` must be integers.

### Symbolic Problem Description

```json
{
    'sym_variables': [('x0', 'reconnaissance troops'), ('x1', 'engineer platoons')],
    'objective_function': 'Minimize 4*x0 + 5*x1',
    'constraints': [
        '16*x0 + 14*x1 >= 81',
        '2*x0 + 1*x1 >= 58',
        '-2*x0 + 7*x1 >= 0',
        '16*x0 + 14*x1 <= 177',
        '2*x0 + 1*x1 <= 116',
        'x0 must be an integer',
        'x1 must be an integer'
    ]
}
```

### Gurobi Code

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="reconnaissance_troops")
x1 = m.addVar(vtype=GRB.INTEGER, name="engineer_platoons")

# Set the objective function
m.setObjective(4*x0 + 5*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(16*x0 + 14*x1 >= 81, "Minimum_Deployment_Weight")
m.addConstr(2*x0 + 1*x1 >= 58, "Minimum_Fun_Factor")
m.addConstr(-2*x0 + 7*x1 >= 0, "Linear_Constraint")
m.addConstr(16*x0 + 14*x1 <= 177, "Maximum_Deployment_Weight")
m.addConstr(2*x0 + 1*x1 <= 116, "Maximum_Fun_Factor")

# Optimize the model
m.optimize()

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

This code defines the optimization problem according to the given symbolic representation and solves it using Gurobi. It then prints out the optimal values for the reconnaissance troops and engineer platoons, along with the objective function value if an optimal solution is found.