## Step 1: Define the symbolic representation of the problem
The problem involves four variables: candles, paper towel rolls, packs of paper plates, and cartons of milk, which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $1 \times \text{candles} + 4 \times \text{paper towel rolls} + 3 \times \text{packs of paper plates} + 1 \times \text{cartons of milk}$, which translates to $x_0 + 4x_1 + 3x_2 + x_3$.

## 3: List the semi-algebraic constraints
The constraints given are:
- $7.91x_0 \geq 6$ (total combined sustainability score from candles)
- However, the correct interpretation is:
  - $7.91x_0 + 2.09x_1 \geq 6$ (sustainability score from candles and paper towel rolls)
  - $2.09x_1 + 0.23x_2 \geq 10$ (sustainability score from paper towel rolls and packs of paper plates)
  - $0.23x_2 + 8.79x_3 \geq 11$ (sustainability score from packs of paper plates and cartons of milk)
  - $2.09x_1 + 0.23x_2 + 8.79x_3 \geq 10$ (sustainability score from paper towel rolls, packs of paper plates, and cartons of milk)
  - $7.91x_0 + 2.09x_1 + 0.23x_2 + 8.79x_3 \geq 10$ (total combined sustainability score)
- Usefulness rating constraints:
  - $2.58x_0 + 1.15x_3 \geq 13$ (usefulness rating from candles and cartons of milk)
  - $1.98x_1 + 1.15x_3 \geq 11$ (usefulness rating from paper towel rolls and cartons of milk)
  - $1.98x_1 + 5.51x_2 \geq 4$ (usefulness rating from paper towel rolls and packs of paper plates)
  - $2.58x_0 + 1.98x_1 + 5.51x_2 + 1.15x_3 \geq 4$ (total combined usefulness rating)
- Additional constraints:
  - $3x_0 - 3x_2 \geq 0$
  - $0.23x_2 + 8.79x_3 \leq 42$ (sustainability score from packs of paper plates and cartons of milk)
  - $7.91x_0 + 2.09x_1 \leq 14$ (sustainability score from candles and paper towel rolls)
  - $7.91x_0 + 8.79x_3 \leq 42$ (sustainability score from candles and cartons of milk)
  - $5.51x_2 + 1.15x_3 \leq 36$ (usefulness rating from packs of paper plates and cartons of milk)
  - $2.58x_0 + 1.98x_1 \leq 21$ (usefulness rating from candles and paper towel rolls)
  - $2.58x_0 + 5.51x_2 \leq 17$ (usefulness rating from candles and packs of paper plates)
  - $1.98x_1 + 5.51x_2 \leq 29$ (usefulness rating from paper towel rolls and packs of paper plates)
- Integrity constraints:
  - $x_0, x_1, x_2, x_3$ are integers.

## 4: Symbolic Representation
The symbolic representation is:
```json
{
  'sym_variables': [('x0', 'candles'), ('x1', 'paper towel rolls'), ('x2', 'packs of paper plates'), ('x3', 'cartons of milk')],
  'objective_function': 'x0 + 4*x1 + 3*x2 + x3',
  'constraints': [
    '7.91*x0 + 2.09*x1 >= 6',
    '2.09*x1 + 0.23*x2 >= 10',
    '0.23*x2 + 8.79*x3 >= 11',
    '2.09*x1 + 0.23*x2 + 8.79*x3 >= 10',
    '7.91*x0 + 2.09*x1 + 0.23*x2 + 8.79*x3 >= 10',
    '2.58*x0 + 1.15*x3 >= 13',
    '1.98*x1 + 1.15*x3 >= 11',
    '1.98*x1 + 5.51*x2 >= 4',
    '2.58*x0 + 1.98*x1 + 5.51*x2 + 1.15*x3 >= 4',
    '3*x0 - 3*x2 >= 0',
    '0.23*x2 + 8.79*x3 <= 42',
    '7.91*x0 + 2.09*x1 <= 14',
    '7.91*x0 + 8.79*x3 <= 42',
    '5.51*x2 + 1.15*x3 <= 36',
    '2.58*x0 + 1.98*x1 <= 21',
    '2.58*x0 + 5.51*x2 <= 17',
    '1.98*x1 + 5.51*x2 <= 29'
  ]
}
```

## 5: Gurobi Code
```python
import gurobi

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

    # Define variables
    candles = model.addVar(name="candles", vtype=gurobi.GRB.INTEGER)
    paper_towel_rolls = model.addVar(name="paper_towel_rolls", vtype=gurobi.GRB.INTEGER)
    packs_of_paper_plates = model.addVar(name="packs_of_paper_plates", vtype=gurobi.GRB.INTEGER)
    cartons_of_milk = model.addVar(name="cartons_of_milk", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(candles + 4 * paper_towel_rolls + 3 * packs_of_paper_plates + cartons_of_milk, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(7.91 * candles + 2.09 * paper_towel_rolls >= 6)
    model.addConstr(2.09 * paper_towel_rolls + 0.23 * packs_of_paper_plates >= 10)
    model.addConstr(0.23 * packs_of_paper_plates + 8.79 * cartons_of_milk >= 11)
    model.addConstr(2.09 * paper_towel_rolls + 0.23 * packs_of_paper_plates + 8.79 * cartons_of_milk >= 10)
    model.addConstr(7.91 * candles + 2.09 * paper_towel_rolls + 0.23 * packs_of_paper_plates + 8.79 * cartons_of_milk >= 10)
    model.addConstr(2.58 * candles + 1.15 * cartons_of_milk >= 13)
    model.addConstr(1.98 * paper_towel_rolls + 1.15 * cartons_of_milk >= 11)
    model.addConstr(1.98 * paper_towel_rolls + 5.51 * packs_of_paper_plates >= 4)
    model.addConstr(2.58 * candles + 1.98 * paper_towel_rolls + 5.51 * packs_of_paper_plates + 1.15 * cartons_of_milk >= 4)
    model.addConstr(3 * candles - 3 * packs_of_paper_plates >= 0)
    model.addConstr(0.23 * packs_of_paper_plates + 8.79 * cartons_of_milk <= 42)
    model.addConstr(7.91 * candles + 2.09 * paper_towel_rolls <= 14)
    model.addConstr(7.91 * candles + 8.79 * cartons_of_milk <= 42)
    model.addConstr(5.51 * packs_of_paper_plates + 1.15 * cartons_of_milk <= 36)
    model.addConstr(2.58 * candles + 1.98 * paper_towel_rolls <= 21)
    model.addConstr(2.58 * candles + 5.51 * packs_of_paper_plates <= 17)
    model.addConstr(1.98 * paper_towel_rolls + 5.51 * packs_of_paper_plates <= 29)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Candles: ", candles.varValue)
        print("Paper Towel Rolls: ", paper_towel_rolls.varValue)
        print("Packs of Paper Plates: ", packs_of_paper_plates.varValue)
        print("Cartons of Milk: ", cartons_of_milk.varValue)
    else:
        print("No solution found")

solve_optimization_problem()
```