## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are ['cornichons', 'protein bars', 'strips of bacon', 'bowls of cereal'], 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 $2 \cdot \text{cornichons} + 7 \cdot \text{protein bars} + 3 \cdot \text{strips of bacon} + 3 \cdot \text{bowls of cereal}$, which translates to $2x_0 + 7x_1 + 3x_2 + 3x_3$.

## 3: List the constraints in symbolic notation
1. $\text{sourness index from protein bars, strips of bacon, and bowls of cereal} \geq 29$: $12x_1 + 14x_2 + x_3 \geq 29$
2. $\text{carbohydrates from strips of bacon and bowls of cereal} \geq 14$: $4x_2 + 7x_3 \geq 14$
3. $\text{fat from protein bars and bowls of cereal} \geq 30$: $9x_1 + 8x_3 \geq 30$
4. $\text{fat from protein bars and strips of bacon} \geq 57$: $9x_1 + 15x_2 \geq 57$
5. $\text{fat from cornichons, strips of bacon, and bowls of cereal} \geq 46$: $15x_0 + 15x_2 + 8x_3 \geq 46$
6. $\text{umami index from cornichons and protein bars} \geq 34$: $16x_0 + 3x_1 \geq 34$
7. $\text{umami index from cornichons and bowls of cereal} \geq 43$: $16x_0 + 3x_3 \geq 43$
8. $\text{umami index from strips of bacon and bowls of cereal} \geq 28$: $13x_2 + 3x_3 \geq 28$
9. $\text{umami index from protein bars, strips of bacon, and bowls of cereal} \geq 33$: $3x_1 + 13x_2 + 3x_3 \geq 33$
10. $\text{sourness index from protein bars and strips of bacon} \leq 88$: $12x_1 + 14x_2 \leq 88$
11. $\text{sourness index from strips of bacon and bowls of cereal} \leq 123$: $14x_2 + x_3 \leq 123$
12. $\text{sourness index from cornichons and bowls of cereal} \leq 63$: $x_0 + x_3 \leq 63$
13. $\text{sourness index from cornichons, protein bars, and bowls of cereal} \leq 96$: $x_0 + 12x_1 + x_3 \leq 96$
14. $\text{sourness index from all} \leq 96$: $x_0 + 12x_1 + 14x_2 + x_3 \leq 96$
15. $\text{carbohydrates from cornichons and protein bars} \leq 115$: $2x_0 + 4x_1 \leq 115$
16. $\text{carbohydrates from cornichons and bowls of cereal} \leq 116$: $2x_0 + 7x_3 \leq 116$
17. $\text{carbohydrates from cornichons, protein bars, and bowls of cereal} \leq 85$: $2x_0 + 4x_1 + 7x_3 \leq 85$
18. $\text{carbohydrates from protein bars, strips of bacon, and bowls of cereal} \leq 101$: $4x_1 + 4x_2 + 7x_3 \leq 101$
19. $\text{carbohydrates from cornichons, protein bars, and strips of bacon} \leq 109$: $2x_0 + 4x_1 + 4x_2 \leq 109$
20. $\text{carbohydrates from all} \leq 109$: $2x_0 + 4x_1 + 4x_2 + 7x_3 \leq 109$
21. $\text{fat from cornichons and bowls of cereal} \leq 183$: $15x_0 + 8x_3 \leq 183$
22. $\text{fat from strips of bacon and bowls of cereal} \leq 98$: $15x_2 + 8x_3 \leq 98$
23. $\text{fat from protein bars and bowls of cereal} \leq 218$: $9x_1 + 8x_3 \leq 218$
24. $\text{fat from cornichons and strips of bacon} \leq 92$: $15x_0 + 15x_2 \leq 92$
25. $\text{fat from all} \leq 92$: $15x_0 + 9x_1 + 15x_2 + 8x_3 \leq 92$
26. $\text{umami index from strips of bacon and bowls of cereal} \leq 158$: $13x_2 + 3x_3 \leq 158$
27. $\text{umami index from protein bars and bowls of cereal} \leq 183$: $3x_1 + 3x_3 \leq 183$
28. $\text{umami index from cornichons and protein bars} \leq 104$: $16x_0 + 3x_1 \leq 104$
29. $\text{umami index from cornichons, strips of bacon, and bowls of cereal} \leq 72$: $16x_0 + 13x_2 + 3x_3 \leq 72$
30. $\text{umami index from all} \leq 72$: $16x_0 + 3x_1 + 13x_2 + 3x_3 \leq 72$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'cornichons'), 
        ('x1', 'protein bars'), 
        ('x2', 'strips of bacon'), 
        ('x3', 'bowls of cereal')
    ], 
    'objective_function': '2*x0 + 7*x1 + 3*x2 + 3*x3', 
    'constraints': [
        '12*x1 + 14*x2 + x3 >= 29',
        '4*x2 + 7*x3 >= 14',
        '9*x1 + 8*x3 >= 30',
        '9*x1 + 15*x2 >= 57',
        '15*x0 + 15*x2 + 8*x3 >= 46',
        '16*x0 + 3*x1 >= 34',
        '16*x0 + 3*x3 >= 43',
        '13*x2 + 3*x3 >= 28',
        '3*x1 + 13*x2 + 3*x3 >= 33',
        '12*x1 + 14*x2 <= 88',
        '14*x2 + x3 <= 123',
        'x0 + x3 <= 63',
        'x0 + 12*x1 + x3 <= 96',
        'x0 + 12*x1 + 14*x2 + x3 <= 96',
        '2*x0 + 4*x1 <= 115',
        '2*x0 + 7*x3 <= 116',
        '2*x0 + 4*x1 + 7*x3 <= 85',
        '4*x1 + 4*x2 + 7*x3 <= 101',
        '2*x0 + 4*x1 + 4*x2 <= 109',
        '2*x0 + 4*x1 + 4*x2 + 7*x3 <= 109',
        '15*x0 + 8*x3 <= 183',
        '15*x2 + 8*x3 <= 98',
        '9*x1 + 8*x3 <= 218',
        '15*x0 + 15*x2 <= 92',
        '15*x0 + 9*x1 + 15*x2 + 8*x3 <= 92',
        '13*x2 + 3*x3 <= 158',
        '3*x1 + 3*x3 <= 183',
        '16*x0 + 3*x1 <= 104',
        '16*x0 + 13*x2 + 3*x3 <= 72',
        '16*x0 + 3*x1 + 13*x2 + 3*x3 <= 72'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name="cornichons", lb=0)
    x1 = model.addVar(name="protein bars", lb=0)
    x2 = model.addVar(name="strips of bacon", lb=0)
    x3 = model.addVar(name="bowls of cereal", lb=0)

    # Define the objective function
    model.setObjective(2*x0 + 7*x1 + 3*x2 + 3*x3, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(12*x1 + 14*x2 + x3 >= 29)
    model.addConstr(4*x2 + 7*x3 >= 14)
    model.addConstr(9*x1 + 8*x3 >= 30)
    model.addConstr(9*x1 + 15*x2 >= 57)
    model.addConstr(15*x0 + 15*x2 + 8*x3 >= 46)
    model.addConstr(16*x0 + 3*x1 >= 34)
    model.addConstr(16*x0 + 3*x3 >= 43)
    model.addConstr(13*x2 + 3*x3 >= 28)
    model.addConstr(3*x1 + 13*x2 + 3*x3 >= 33)
    model.addConstr(12*x1 + 14*x2 <= 88)
    model.addConstr(14*x2 + x3 <= 123)
    model.addConstr(x0 + x3 <= 63)
    model.addConstr(x0 + 12*x1 + x3 <= 96)
    model.addConstr(x0 + 12*x1 + 14*x2 + x3 <= 96)
    model.addConstr(2*x0 + 4*x1 <= 115)
    model.addConstr(2*x0 + 7*x3 <= 116)
    model.addConstr(2*x0 + 4*x1 + 7*x3 <= 85)
    model.addConstr(4*x1 + 4*x2 + 7*x3 <= 101)
    model.addConstr(2*x0 + 4*x1 + 4*x2 <= 109)
    model.addConstr(2*x0 + 4*x1 + 4*x2 + 7*x3 <= 109)
    model.addConstr(15*x0 + 8*x3 <= 183)
    model.addConstr(15*x2 + 8*x3 <= 98)
    model.addConstr(9*x1 + 8*x3 <= 218)
    model.addConstr(15*x0 + 15*x2 <= 92)
    model.addConstr(15*x0 + 9*x1 + 15*x2 + 8*x3 <= 92)
    model.addConstr(13*x2 + 3*x3 <= 158)
    model.addConstr(3*x1 + 3*x3 <= 183)
    model.addConstr(16*x0 + 3*x1 <= 104)
    model.addConstr(16*x0 + 13*x2 + 3*x3 <= 72)
    model.addConstr(16*x0 + 3*x1 + 13*x2 + 3*x3 <= 72)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("cornichons: ", x0.varValue)
        print("protein bars: ", x1.varValue)
        print("strips of bacon: ", x2.varValue)
        print("bowls of cereal: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```