To solve the optimization problem described, we first need to establish a clear symbolic representation of the variables and constraints involved. The variables are 'packs of napkins' and 'paper towel rolls', which can be represented symbolically as \(x_1\) and \(x_2\), respectively.

The objective function aims to minimize \(4.42x_1 + 5.02x_2\).

Given the constraints:
1. Packs of napkins are worth $7 each, and paper towel rolls are worth $8 each.
2. The combined value of packs of napkins and paper towel rolls must be at least $16.
3. This constraint is repeated, so it's considered only once.
4. \(-5x_1 + 3x_2 \geq 0\).
5. The total value of both items must not exceed $39.
6. Both \(x_1\) and \(x_2\) must be whole numbers.

Thus, the symbolic representation of the problem is:
```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'
    ]
}
```

To solve this problem using Gurobi, we'll write the Python code to model and solve the optimization problem:

```python
from gurobipy import *

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

# Add variables to the model
x1 = m.addVar(vtype=GRB.INTEGER, name="packs_of_napkins")
x2 = m.addVar(vtype=GRB.INTEGER, name="paper_towel_rolls")

# Set the objective function
m.setObjective(4.42*x1 + 5.02*x2, GRB.MINIMIZE)

# Add constraints to the model
m.addConstr(7*x1 + 8*x2 >= 16, "combined_value_at_least")
m.addConstr(-5*x1 + 3*x2 >= 0, "napkins_and_rolls_constraint")
m.addConstr(7*x1 + 8*x2 <= 39, "total_value_not_exceed")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Packs of Napkins: {x1.x}")
    print(f"Paper Towel Rolls: {x2.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```