To solve this problem, we need to break down the given information into a symbolic representation and then formulate it in Gurobi code. The variables are 'packs of napkins' and 'dish soap bottles'. Let's denote these as $x_0$ for packs of napkins and $x_1$ for dish soap bottles.

The objective function is to minimize $4x_0 + x_1$, which represents the total cost where each pack of napkins costs 4 units (but this seems to contradict the given problem statement where it's mentioned that packs of napkins are $3 each and so are dish soap bottles; for consistency with the rest of the problem description, we'll proceed with the costs as described in the constraints).

The constraints can be summarized as follows:
1. Dollar cost constraint: $3x_0 + 3x_1 \geq 16$ (minimum spend) and $3x_0 + 3x_1 \leq 32$ (maximum spend).
2. Usefulness rating constraint: $x_0 + 8x_1 \geq 8$ (minimum usefulness) and $x_0 + 8x_1 \leq 26$ (maximum usefulness).
3. Sustainability score constraint: $x_0 + x_1 \geq 13$ (minimum sustainability) and $x_0 + x_1 \leq 32$ (maximum sustainability).
4. Additional constraint: $-x_0 + 2x_1 \geq 0$.
5. Non-negativity and integer constraints: $x_0, x_1 \geq 0$ and $x_0, x_1$ are integers.

Here is the symbolic representation:
```json
{
  'sym_variables': [('x0', 'packs of napkins'), ('x1', 'dish soap bottles')],
  'objective_function': '4*x0 + x1',
  'constraints': [
    '3*x0 + 3*x1 >= 16',
    '3*x0 + 3*x1 <= 32',
    'x0 + 8*x1 >= 8',
    'x0 + 8*x1 <= 26',
    'x0 + x1 >= 13',
    'x0 + x1 <= 32',
    '-x0 + 2*x1 >= 0',
    'x0 >= 0',
    'x1 >= 0'
  ]
}
```

Given the confusion in the objective function's coefficients and the problem statement, we will adjust our Gurobi code to reflect the costs as described in the constraints ($3 for each item) but use the objective function provided directly from the problem description (4 times packs of napkins plus 1 times dish soap bottles).

```python
from gurobipy import *

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

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

# Objective function
m.setObjective(4*x0 + x1, GRB.MINIMIZE)

# Constraints
m.addConstr(3*x0 + 3*x1 >= 16, "minimum_spend")
m.addConstr(3*x0 + 3*x1 <= 32, "maximum_spend")
m.addConstr(x0 + 8*x1 >= 8, "minimum_usefulness")
m.addConstr(x0 + 8*x1 <= 26, "maximum_usefulness")
m.addConstr(x0 + x1 >= 13, "minimum_sustainability")
m.addConstr(x0 + x1 <= 32, "maximum_sustainability")
m.addConstr(-x0 + 2*x1 >= 0, "additional_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Packs of napkins: {x0.x}")
    print(f"Dish soap bottles: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```