## Problem Description and Symbolic Representation

The problem involves minimizing an objective function subject to several constraints. The variables are 'reconnaissance troops' and 'engineer platoons', denoted as $x_1$ and $x_2$ respectively.

### Symbolic Representation

* Variables: 
  - $x_1$ : reconnaissance troops
  - $x_2$ : engineer platoons

* Objective Function: $4x_1 + 5x_2$

* Constraints:
  1. $16x_1 + 14x_2 \geq 81$
  2. $2x_1 + x_2 \geq 58$
  3. $-2x_1 + 7x_2 \geq 0$
  4. $16x_1 + 14x_2 \leq 163$
  5. $2x_1 + x_2 \leq 116$
  6. $x_1 \in \mathbb{Z}^+$
  7. $x_2 \in \mathbb{Z}^+$

## Gurobi Code

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define variables
x1 = model.addVar(name="reconnaissance_troops", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="engineer_platoons", vtype=gurobi.GRB.INTEGER)

# Objective function
model.setObjective(4 * x1 + 5 * x2, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(16 * x1 + 14 * x2 >= 81, name="deployment_weight_min")
model.addConstr(2 * x1 + x2 >= 58, name="fun_factor_min")
model.addConstr(-2 * x1 + 7 * x2 >= 0, name="troops_platoons_balance")
model.addConstr(16 * x1 + 14 * x2 <= 163, name="deployment_weight_max")
model.addConstr(2 * x1 + x2 <= 116, name="fun_factor_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Reconnaissance troops: {x1.varValue}")
    print(f"Engineer platoons: {x2.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```

## Solution in JSON Format

```json
{
  "sym_variables": [
    ["x1", "reconnaissance troops"],
    ["x2", "engineer platoons"]
  ],
  "objective_function": "4*x1 + 5*x2",
  "constraints": [
    "16*x1 + 14*x2 >= 81",
    "2*x1 + x2 >= 58",
    "-2*x1 + 7*x2 >= 0",
    "16*x1 + 14*x2 <= 163",
    "2*x1 + x2 <= 116",
    "x1 \u2208 \u2124^+",
    "x2 \u2208 \u2124^+"
  ]
}
```