## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'diapers', 'packs of napkins', 'bottles of ibuprofen', and 'packs of paper plates', which we can denote as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $5.02x_0 + 2.81x_1 + 8.52x_2 + 9.37x_3$.

## 3: List the constraints in symbolic notation
1. $6.1x_0 \leq 330$
2. $9.5x_0 \leq 262$
3. $0.53x_0 \leq 246$
4. $1.45x_1 \leq 330$
5. $2.37x_1 \leq 262$
6. $10.77x_1 \leq 246$
7. $13.13x_2 \leq 330$
8. $4.94x_2 \leq 262$
9. $14.72x_2 \leq 246$
10. $15.03x_3 \leq 330$
11. $9.82x_3 \leq 262$
12. $7.51x_3 \leq 246$
13. $13.13x_2 + 15.03x_3 \geq 74$
14. $2.37x_1 + 9.82x_3 \geq 42$
15. $9.5x_0 + 4.94x_2 + 9.82x_3 \geq 33$
16. $9.5x_0 + 2.37x_1 + 4.94x_2 \geq 33$
17. $9.5x_0 + 4.94x_2 + 9.82x_3 \geq 33$
18. $9.5x_0 + 2.37x_1 + 4.94x_2 \geq 63$
19. $2.37x_1 + 4.94x_2 + 9.82x_3 \geq 63$
20. $9.5x_0 + 4.94x_2 + 9.82x_3 \geq 58$
21. $9.5x_0 + 2.37x_1 + 4.94x_2 \geq 58$
22. $2.37x_1 + 4.94x_2 + 9.82x_3 \geq 58$
23. $9.5x_0 + 4.94x_2 + 9.82x_3 \geq 59$
24. $1.45x_1 + 15.03x_3 \leq 126$
25. $13.13x_2 + 15.03x_3 \leq 230$
26. $6.1x_0 + 15.03x_3 \leq 90$
27. $1.45x_1 + 13.13x_2 \leq 300$
28. $6.1x_0 + 1.45x_1 + 13.13x_2 \leq 229$
29. $6.1x_0 + 1.45x_1 + 13.13x_2 + 15.03x_3 \leq 229$
30. $9.5x_0 + 2.37x_1 \leq 148$
31. $9.5x_0 + 9.82x_3 \leq 125$
32. $4.94x_2 + 9.82x_3 \leq 73$
33. $2.37x_1 + 4.94x_2 \leq 252$
34. $9.5x_0 + 2.37x_1 + 4.94x_2 + 9.82x_3 \leq 252$
35. $9.5x_0 + 4.94x_2 \leq 219$
36. $2.37x_1 + 9.82x_3 \leq 240$
37. $9.5x_0 + 9.82x_3 \leq 174$
38. $2.37x_1 + 4.94x_2 \leq 119$
39. $4.94x_2 + 9.82x_3 \leq 176$
40. $9.5x_0 + 2.37x_1 + 4.94x_2 \leq 140$
41. $9.5x_0 + 2.37x_1 + 4.94x_2 + 9.82x_3 \leq 140$

## 4: Define the symbolic variables and constraints for the JSON output
```json
{
    "sym_variables": [
        ["x0", "diapers"],
        ["x1", "packs of napkins"],
        ["x2", "bottles of ibuprofen"],
        ["x3", "packs of paper plates"]
    ],
    "objective_function": "5.02x0 + 2.81x1 + 8.52x2 + 9.37x3",
    "constraints": [
        "6.1x0 <= 330",
        "9.5x0 <= 262",
        "0.53x0 <= 246",
        "1.45x1 <= 330",
        "2.37x1 <= 262",
        "10.77x1 <= 246",
        "13.13x2 <= 330",
        "4.94x2 <= 262",
        "14.72x2 <= 246",
        "15.03x3 <= 330",
        "9.82x3 <= 262",
        "7.51x3 <= 246",
        "13.13x2 + 15.03x3 >= 74",
        "2.37x1 + 9.82x3 >= 42",
        "9.5x0 + 4.94x2 + 9.82x3 >= 33",
        "9.5x0 + 2.37x1 + 4.94x2 >= 33",
        "9.5x0 + 4.94x2 + 9.82x3 >= 33",
        "9.5x0 + 2.37x1 + 4.94x2 >= 63",
        "2.37x1 + 4.94x2 + 9.82x3 >= 63",
        "9.5x0 + 4.94x2 + 9.82x3 >= 58",
        "9.5x0 + 2.37x1 + 4.94x2 >= 58",
        "2.37x1 + 4.94x2 + 9.82x3 >= 58",
        "9.5x0 + 4.94x2 + 9.82x3 >= 59",
        "1.45x1 + 15.03x3 <= 126",
        "13.13x2 + 15.03x3 <= 230",
        "6.1x0 + 15.03x3 <= 90",
        "1.45x1 + 13.13x2 <= 300",
        "6.1x0 + 1.45x1 + 13.13x2 <= 229",
        "6.1x0 + 1.45x1 + 13.13x2 + 15.03x3 <= 229",
        "9.5x0 + 2.37x1 <= 148",
        "9.5x0 + 9.82x3 <= 125",
        "4.94x2 + 9.82x3 <= 73",
        "2.37x1 + 4.94x2 <= 252",
        "9.5x0 + 2.37x1 + 4.94x2 + 9.82x3 <= 252",
        "9.5x0 + 4.94x2 <= 219",
        "2.37x1 + 9.82x3 <= 240",
        "9.5x0 + 9.82x3 <= 174",
        "2.37x1 + 4.94x2 <= 119",
        "4.94x2 + 9.82x3 <= 176",
        "9.5x0 + 2.37x1 + 4.94x2 <= 140",
        "9.5x0 + 2.37x1 + 4.94x2 + 9.82x3 <= 140",
        "x0 % 1 == 0",
        "x1 % 1 == 0",
        "x2 % 1 == 0",
        "x3 % 1 == 0"
    ]
}
```

## 5: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="diapers", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="packs of napkins", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="bottles of ibuprofen", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="packs of paper plates", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(5.02*x0 + 2.81*x1 + 8.52*x2 + 9.37*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6.1*x0 <= 330)
    model.addConstr(9.5*x0 <= 262)
    model.addConstr(0.53*x0 <= 246)
    model.addConstr(1.45*x1 <= 330)
    model.addConstr(2.37*x1 <= 262)
    model.addConstr(10.77*x1 <= 246)
    model.addConstr(13.13*x2 <= 330)
    model.addConstr(4.94*x2 <= 262)
    model.addConstr(14.72*x2 <= 246)
    model.addConstr(15.03*x3 <= 330)
    model.addConstr(9.82*x3 <= 262)
    model.addConstr(7.51*x3 <= 246)
    model.addConstr(13.13*x2 + 15.03*x3 >= 74)
    model.addConstr(2.37*x1 + 9.82*x3 >= 42)
    model.addConstr(9.5*x0 + 4.94*x2 + 9.82*x3 >= 33)
    model.addConstr(9.5*x0 + 2.37*x1 + 4.94*x2 >= 33)
    model.addConstr(9.5*x0 + 4.94*x2 + 9.82*x3 >= 33)
    model.addConstr(9.5*x0 + 2.37*x1 + 4.94*x2 >= 63)
    model.addConstr(2.37*x1 + 4.94*x2 + 9.82*x3 >= 63)
    model.addConstr(9.5*x0 + 4.94*x2 + 9.82*x3 >= 58)
    model.addConstr(9.5*x0 + 2.37*x1 + 4.94*x2 >= 58)
    model.addConstr(2.37*x1 + 4.94*x2 + 9.82*x3 >= 58)
    model.addConstr(9.5*x0 + 4.94*x2 + 9.82*x3 >= 59)
    model.addConstr(1.45*x1 + 15.03*x3 <= 126)
    model.addConstr(13.13*x2 + 15.03*x3 <= 230)
    model.addConstr(6.1*x0 + 15.03*x3 <= 90)
    model.addConstr(1.45*x1 + 13.13*x2 <= 300)
    model.addConstr(6.1*x0 + 1.45*x1 + 13.13*x2 <= 229)
    model.addConstr(6.1*x0 + 1.45*x1 + 13.13*x2 + 15.03*x3 <= 229)
    model.addConstr(9.5*x0 + 2.37*x1 <= 148)
    model.addConstr(9.5*x0 + 9.82*x3 <= 125)
    model.addConstr(4.94*x2 + 9.82*x3 <= 73)
    model.addConstr(2.37*x1 + 4.94*x2 <= 252)
    model.addConstr(9.5*x0 + 2.37*x1 + 4.94*x2 + 9.82*x3 <= 252)
    model.addConstr(9.5*x0 + 4.94*x2 <= 219)
    model.addConstr(2.37*x1 + 9.82*x3 <= 240)
    model.addConstr(9.5*x0 + 9.82*x3 <= 174)
    model.addConstr(2.37*x1 + 4.94*x2 <= 119)
    model.addConstr(4.94*x2 + 9.82*x3 <= 176)
    model.addConstr(9.5*x0 + 2.37*x1 + 4.94*x2 <= 140)
    model.addConstr(9.5*x0 + 2.37*x1 + 4.94*x2 + 9.82*x3 <= 140)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Diapers: ", x0.varValue)
        print("Packs of napkins: ", x1.varValue)
        print("Bottles of ibuprofen: ", x2.varValue)
        print("Packs of paper plates: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```