## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- 'candles' corresponds to 'x1'
- 'dish soap bottles' corresponds to 'x2'
- 'bottles of ibuprofen' corresponds to 'x3'
- 'toilet paper rolls' corresponds to 'x4'

## Step 2: Define the symbolic representation of the problem
The symbolic representation of the variables is:
```json
{
'sym_variables': [
    ('x1', 'candles'), 
    ('x2', 'dish soap bottles'), 
    ('x3', 'bottles of ibuprofen'), 
    ('x4', 'toilet paper rolls')
]
}
```

## Step 3: Determine the objective function
The objective function to maximize is: 
\[ 5.11x_1 + 5.61x_2 + 1.51x_3 + 8.4x_4 \]

## Step 4: List the constraints
The constraints are:
- \( 21x_1 + 10x_3 \geq 12 \) (combined weight of candles and bottles of ibuprofen)
- \( 21x_1 + 16x_2 + 6x_4 \geq 22 \) (total weight of candles, dish soap bottles, and toilet paper rolls)
- \( 21x_1 + 16x_2 \leq 88 \) (combined weight of candles and dish soap bottles)
- \( 21x_1 + 6x_4 \leq 129 \) (combined weight of candles and toilet paper rolls)
- \( 16x_2 + 10x_3 \leq 129 \) (combined weight of dish soap bottles and bottles of ibuprofen)
- \( 10x_3 + 6x_4 \leq 116 \) (combined weight of bottles of ibuprofen and toilet paper rolls)
- \( 21x_1 + 16x_2 + 6x_4 \leq 140 \) (total weight of candles, dish soap bottles, and toilet paper rolls)
- \( 21x_1 + 16x_2 + 10x_3 + 6x_4 \leq 151 \) (total weight of all items)
- \( 5x_1 + 7x_2 \leq 126 \) (combined sustainability score of candles and dish soap bottles)
- \( 5x_1 + 15x_4 \leq 95 \) (combined sustainability score of candles and toilet paper rolls)
- \( 5x_1 + 22x_3 + 15x_4 \leq 79 \) (combined sustainability score of candles, bottles of ibuprofen, and toilet paper rolls)
- \( 5x_1 + 7x_2 + 22x_3 + 15x_4 \leq 79 \) (combined sustainability score of all items)
- \( x_1, x_2, x_3, x_4 \geq 0 \) and are integers.

## 5: Write down the complete symbolic problem representation
```json
{
'sym_variables': [
    ('x1', 'candles'), 
    ('x2', 'dish soap bottles'), 
    ('x3', 'bottles of ibuprofen'), 
    ('x4', 'toilet paper rolls')
],
'objective_function': '5.11*x1 + 5.61*x2 + 1.51*x3 + 8.4*x4',
'constraints': [
    '21*x1 + 10*x3 >= 12',
    '21*x1 + 16*x2 + 6*x4 >= 22',
    '21*x1 + 16*x2 <= 88',
    '21*x1 + 6*x4 <= 129',
    '16*x2 + 10*x3 <= 129',
    '10*x3 + 6*x4 <= 116',
    '21*x1 + 16*x2 + 6*x4 <= 140',
    '21*x1 + 16*x2 + 10*x3 + 6*x4 <= 151',
    '5*x1 + 7*x2 <= 126',
    '5*x1 + 15*x4 <= 95',
    '5*x1 + 22*x3 + 15*x4 <= 79',
    '5*x1 + 7*x2 + 22*x3 + 15*x4 <= 79',
    'x1, x2, x3, x4 >= 0 and are integers'
]
}
```

## 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="candles", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="dish_soap_bottles", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="bottles_of_ibuprofen", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="toilet_paper_rolls", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(5.11*x1 + 5.61*x2 + 1.51*x3 + 8.4*x4, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(21*x1 + 10*x3 >= 12)
    model.addConstr(21*x1 + 16*x2 + 6*x4 >= 22)
    model.addConstr(21*x1 + 16*x2 <= 88)
    model.addConstr(21*x1 + 6*x4 <= 129)
    model.addConstr(16*x2 + 10*x3 <= 129)
    model.addConstr(10*x3 + 6*x4 <= 116)
    model.addConstr(21*x1 + 16*x2 + 6*x4 <= 140)
    model.addConstr(21*x1 + 16*x2 + 10*x3 + 6*x4 <= 151)
    model.addConstr(5*x1 + 7*x2 <= 126)
    model.addConstr(5*x1 + 15*x4 <= 95)
    model.addConstr(5*x1 + 22*x3 + 15*x4 <= 79)
    model.addConstr(5*x1 + 7*x2 + 22*x3 + 15*x4 <= 79)

    # Set bounds for variables
    model.addConstr(x1 >= 0)
    model.addConstr(x2 >= 0)
    model.addConstr(x3 >= 0)
    model.addConstr(x4 >= 0)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Candles: {x1.varValue}")
        print(f"Dish soap bottles: {x2.varValue}")
        print(f"Bottles of ibuprofen: {x3.varValue}")
        print(f"Toilet paper rolls: {x4.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```