## Step 1: Define the symbolic representation of the problem
The problem involves four variables: 'bottles of ibuprofen', 'toilet paper rolls', 'cookies', and 'lightbulbs', which we can denote as $x_0, x_1, x_2,$ and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $8x_0 + 2x_1 + 9x_2 + x_3$.

## Step 3: List the constraints in symbolic notation
The constraints given are:
1. $8x_0 \geq 8$ (usefulness rating of bottles of ibuprofen)
2. $10x_0 \leq 182$ (storage space of bottles of ibuprofen)
3. $14x_1 \leq 208$ (usefulness rating of toilet paper rolls)
4. $13x_1 \leq 182$ (storage space of toilet paper rolls)
5. $7x_2 \leq 208$ (usefulness rating of cookies)
6. $8x_2 \leq 182$ (storage space of cookies)
7. $7x_3 \leq 208$ (usefulness rating of lightbulbs)
8. $6x_3 \leq 182$ (storage space of lightbulbs)
9. $8x_0 + 7x_2 \geq 36$ (combined usefulness rating from bottles of ibuprofen and cookies)
10. $8x_0 + 7x_3 \geq 47$ (combined usefulness rating from bottles of ibuprofen and lightbulbs)
11. $8x_0 + 14x_1 + 7x_3 \geq 29$ (combined usefulness rating from bottles of ibuprofen, toilet paper rolls, and lightbulbs)
12. $14x_1 + 7x_2 + 7x_3 \geq 29$ (combined usefulness rating from toilet paper rolls, cookies, and lightbulbs)
13. $8x_0 + 14x_1 + 7x_3 \geq 35$ (another combined usefulness rating)
14. $14x_1 + 7x_2 + 7x_3 \geq 35$ (another combined usefulness rating)
15. $8x_0 + 14x_1 + 7x_2 + 7x_3 \geq 35$ (combined usefulness rating from all items)
16. $8x_2 + 6x_3 \geq 43$ (storage space from cookies and lightbulbs)
17. $10x_0 + 8x_2 \geq 31$ (storage space from bottles of ibuprofen and cookies)
18. $10x_0 + 13x_1 \geq 19$ (storage space from bottles of ibuprofen and toilet paper rolls)
19. $13x_1 + 8x_2 + 6x_3 \geq 38$ (storage space from toilet paper rolls, cookies, and lightbulbs)
20. $10x_0 + 13x_1 + 6x_3 \geq 38$ (storage space from bottles of ibuprofen, toilet paper rolls, and lightbulbs)
21. $13x_1 + 8x_2 + 6x_3 \geq 29$ (another storage space constraint)
22. $10x_0 + 13x_1 + 6x_3 \geq 29$ (another storage space constraint)
23. $10x_0 + 13x_1 + 8x_2 + 6x_3 \geq 29$ (storage space from all items)
24. $5x_1 - 2x_3 \geq 0$ (relationship between toilet paper rolls and lightbulbs)
25. $8x_2 + 6x_3 \leq 74$ (storage space limit from cookies and lightbulbs)
26. $10x_0 + 13x_1 + 6x_3 \leq 77$ (storage space limit from bottles of ibuprofen, toilet paper rolls, and lightbulbs)
27. $10x_0 + 8x_2 + 6x_3 \leq 96$ (storage space limit from bottles of ibuprofen, cookies, and lightbulbs)

## 4: Define the symbolic variables and constraints for the JSON output
```json
{
    'sym_variables': [
        ('x0', 'bottles of ibuprofen'),
        ('x1', 'toilet paper rolls'),
        ('x2', 'cookies'),
        ('x3', 'lightbulbs')
    ],
    'objective_function': '8*x0 + 2*x1 + 9*x2 + x3',
    'constraints': [
        '8*x0 >= 8',
        '10*x0 <= 182',
        '14*x1 <= 208',
        '13*x1 <= 182',
        '7*x2 <= 208',
        '8*x2 <= 182',
        '7*x3 <= 208',
        '6*x3 <= 182',
        '8*x0 + 7*x2 >= 36',
        '8*x0 + 7*x3 >= 47',
        '8*x0 + 14*x1 + 7*x3 >= 29',
        '14*x1 + 7*x2 + 7*x3 >= 29',
        '8*x0 + 14*x1 + 7*x3 >= 35',
        '14*x1 + 7*x2 + 7*x3 >= 35',
        '8*x0 + 14*x1 + 7*x2 + 7*x3 >= 35',
        '8*x2 + 6*x3 >= 43',
        '10*x0 + 8*x2 >= 31',
        '10*x0 + 13*x1 >= 19',
        '13*x1 + 8*x2 + 6*x3 >= 38',
        '10*x0 + 13*x1 + 6*x3 >= 38',
        '13*x1 + 8*x2 + 6*x3 >= 29',
        '10*x0 + 13*x1 + 6*x3 >= 29',
        '10*x0 + 13*x1 + 8*x2 + 6*x3 >= 29',
        '5*x1 - 2*x3 >= 0',
        '8*x2 + 6*x3 <= 74',
        '10*x0 + 13*x1 + 6*x3 <= 77',
        '10*x0 + 8*x2 + 6*x3 <= 96'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name='x0', vtype=gurobi.GRB.INTEGER)  # bottles of ibuprofen
x1 = m.addVar(name='x1', vtype=gurobi.GRB.INTEGER)  # toilet paper rolls
x2 = m.addVar(name='x2', vtype=gurobi.GRB.INTEGER)  # cookies
x3 = m.addVar(name='x3', vtype=gurobi.GRB.INTEGER)  # lightbulbs

# Define the objective function
m.setObjective(8*x0 + 2*x1 + 9*x2 + x3, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(8*x0 >= 8)
m.addConstr(10*x0 <= 182)
m.addConstr(14*x1 <= 208)
m.addConstr(13*x1 <= 182)
m.addConstr(7*x2 <= 208)
m.addConstr(8*x2 <= 182)
m.addConstr(7*x3 <= 208)
m.addConstr(6*x3 <= 182)
m.addConstr(8*x0 + 7*x2 >= 36)
m.addConstr(8*x0 + 7*x3 >= 47)
m.addConstr(8*x0 + 14*x1 + 7*x3 >= 29)
m.addConstr(14*x1 + 7*x2 + 7*x3 >= 29)
m.addConstr(8*x0 + 14*x1 + 7*x3 >= 35)
m.addConstr(14*x1 + 7*x2 + 7*x3 >= 35)
m.addConstr(8*x0 + 14*x1 + 7*x2 + 7*x3 >= 35)
m.addConstr(8*x2 + 6*x3 >= 43)
m.addConstr(10*x0 + 8*x2 >= 31)
m.addConstr(10*x0 + 13*x1 >= 19)
m.addConstr(13*x1 + 8*x2 + 6*x3 >= 38)
m.addConstr(10*x0 + 13*x1 + 6*x3 >= 38)
m.addConstr(13*x1 + 8*x2 + 6*x3 >= 29)
m.addConstr(10*x0 + 13*x1 + 6*x3 >= 29)
m.addConstr(10*x0 + 13*x1 + 8*x2 + 6*x3 >= 29)
m.addConstr(5*x1 - 2*x3 >= 0)
m.addConstr(8*x2 + 6*x3 <= 74)
m.addConstr(10*x0 + 13*x1 + 6*x3 <= 77)
m.addConstr(10*x0 + 8*x2 + 6*x3 <= 96)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objval)
    print('x0: ', x0.varValue)
    print('x1: ', x1.varValue)
    print('x2: ', x2.varValue)
    print('x3: ', x3.varValue)
else:
    print('No optimal solution found')
```