## Step 1: Define the symbolic representation of the variables
The variables are 'dish soap bottles', 'bottles of ibuprofen', 'diapers', and 'lightbulbs', which can be represented symbolically as $x_1, x_2, x_3,$ and $x_4$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The objective function to maximize is $3x_1 + 1x_2 + 9x_3 + 2x_4$.

## Step 3: List the constraints in symbolic notation
The constraints given are:
- $20.33x_3 + 1.14x_4 \geq 76$
- $5.02x_1 + 20.33x_3 \geq 52$
- $13.37x_2 + 20.33x_3 \leq 146$
- $13.37x_2 + 1.14x_4 \leq 292$
- $5.02x_1 + 13.37x_2 \leq 208$
- $5.02x_1 + 1.14x_4 \leq 163$
- $13.37x_2 + 20.33x_3 + 1.14x_4 \leq 206$
- $5.02x_1 + 13.37x_2 + 20.33x_3 + 1.14x_4 \leq 395$
- $x_1, x_2, x_3, x_4$ are integers.

## 4: Define the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'dish soap bottles'), ('x2', 'bottles of ibuprofen'), ('x3', 'diapers'), ('x4', 'lightbulbs')],
'objective_function': '3*x1 + 1*x2 + 9*x3 + 2*x4',
'constraints': [
    '20.33*x3 + 1.14*x4 >= 76',
    '5.02*x1 + 20.33*x3 >= 52',
    '13.37*x2 + 20.33*x3 <= 146',
    '13.37*x2 + 1.14*x4 <= 292',
    '5.02*x1 + 13.37*x2 <= 208',
    '5.02*x1 + 1.14*x4 <= 163',
    '13.37*x2 + 20.33*x3 + 1.14*x4 <= 206',
    '5.02*x1 + 13.37*x2 + 20.33*x3 + 1.14*x4 <= 395'
]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='dish_soap_bottles', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='bottles_of_ibuprofen', vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name='diapers', vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name='lightbulbs', vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(3*x1 + x2 + 9*x3 + 2*x4, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(20.33*x3 + 1.14*x4 >= 76)
    model.addConstr(5.02*x1 + 20.33*x3 >= 52)
    model.addConstr(13.37*x2 + 20.33*x3 <= 146)
    model.addConstr(13.37*x2 + 1.14*x4 <= 292)
    model.addConstr(5.02*x1 + 13.37*x2 <= 208)
    model.addConstr(5.02*x1 + 1.14*x4 <= 163)
    model.addConstr(13.37*x2 + 20.33*x3 + 1.14*x4 <= 206)
    model.addConstr(5.02*x1 + 13.37*x2 + 20.33*x3 + 1.14*x4 <= 395)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('dish soap bottles: ', x1.varValue)
        print('bottles of ibuprofen: ', x2.varValue)
        print('diapers: ', x3.varValue)
        print('lightbulbs: ', x4.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```