## Step 1: Define the symbolic representation of the variables
The variables are 'packs of napkins' and 'paper towel rolls', 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 minimize is $4.42x_1 + 5.02x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $7x_1 + 8x_2 \geq 16$
2. $7x_1 + 8x_2 \geq 16$ ( duplicate of the first constraint)
3. $-5x_1 + 3x_2 \geq 0$
4. $7x_1 + 8x_2 \leq 39$
5. $x_1$ is an integer (whole number of packs of napkins)
6. $x_2$ is an integer (non-fractional amount of paper towel rolls)

## 4: Remove duplicate constraints
Removing the duplicate constraint, we have:
1. $7x_1 + 8x_2 \geq 16$
2. $-5x_1 + 3x_2 \geq 0$
3. $7x_1 + 8x_2 \leq 39$
And the integrality constraints.

## 5: Write down the complete symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'packs of napkins'), ('x2', 'paper towel rolls')],
'objective_function': '4.42*x1 + 5.02*x2',
'constraints': [
    '7*x1 + 8*x2 >= 16',
    '-5*x1 + 3*x2 >= 0',
    '7*x1 + 8*x2 <= 39',
    'x1 is an integer',
    'x2 is an integer'
]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="packs_of_napkins", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="paper_towel_rolls", vtype=gurobi.GRB.INTEGER)

    # Objective function: minimize 4.42*x1 + 5.02*x2
    model.setObjective(4.42*x1 + 5.02*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(7*x1 + 8*x2 >= 16)
    model.addConstr(-5*x1 + 3*x2 >= 0)
    model.addConstr(7*x1 + 8*x2 <= 39)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Packs of napkins: {x1.varValue}")
        print(f"Paper towel rolls: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```