## Step 1: Define the symbolic representation of the variables
The variables are 'military intelligence companies' and 'mechanized infantry companies', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $2.69x_1 + 8.87x_2$.

## Step 3: Convert the constraints into a symbolic representation
The constraints are:
1. $0.52x_1 + 0.27x_2 \geq 45$ (deployment weight of at least 45 metric tons, but the problem states it must be at least 45, however, another constraint $0.52x_1 + 0.27x_2 \leq 117$ is given, and it seems there was an intention to limit the total, so we consider both)
2. $0.16x_1 + 0.03x_2 \geq 41$ (total combined logistical capacity from military intelligence companies plus mechanized infantry companies should be at least 41)
3. $-2x_1 + 10x_2 \geq 0$ (minus two times the number of military intelligence companies, plus ten times the number of mechanized infantry companies has to be no less than zero)
4. $0.52x_1 + 0.27x_2 \leq 117$ (total combined deployment weight of at most 117 metric tons)
5. $0.16x_1 + 0.03x_2 \leq 57$ (total combined logistical capacity from military intelligence companies, and mechanized infantry companies should be equal to or less than 57)
6. $x_1, x_2$ are integers (whole number of military intelligence companies and mechanized infantry companies)

## 4: Define the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'military intelligence companies'), ('x2', 'mechanized infantry companies')],
'objective_function': '2.69*x1 + 8.87*x2',
'constraints': [
    '0.52*x1 + 0.27*x2 >= 45',
    '0.16*x1 + 0.03*x2 >= 41',
    '-2*x1 + 10*x2 >= 0',
    '0.52*x1 + 0.27*x2 <= 117',
    '0.16*x1 + 0.03*x2 <= 57',
    'x1 >= 0',
    'x2 >= 0',
    'x1 % 1 == 0',
    'x2 % 1 == 0'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x1 = m.addVar(name="military_intelligence_companies", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="mechanized_infantry_companies", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(2.69*x1 + 8.87*x2, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(0.52*x1 + 0.27*x2 >= 45, name="deployment_weight_min")
m.addConstr(0.16*x1 + 0.03*x2 >= 41, name="logistical_capacity_min")
m.addConstr(-2*x1 + 10*x2 >= 0, name="mechanized_infantry_companies_vs_military_intelligence_companies")
m.addConstr(0.52*x1 + 0.27*x2 <= 117, name="deployment_weight_max")
m.addConstr(0.16*x1 + 0.03*x2 <= 57, name="logistical_capacity_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Military intelligence companies: {x1.varValue}")
    print(f"Mechanized infantry companies: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```