## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'cornichons', 'apples', and 'rotisserie chickens', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $9.55x_0 + 6.3x_1 + 2.65x_2$.

## 3: List the constraints in symbolic notation
The constraints given are:
1. $x_0 \geq 0$, $x_1 \geq 0$, $x_2 \geq 0$ (non-negativity constraints, though $x_2$ must be an integer)
2. $3x_0 + x_1 + 3x_2 \leq 143$ (iron constraint)
3. $6x_0 + 6x_1 + 7x_2 \leq 175$ (umami index constraint)
4. $x_1 + 3x_2 \geq 47$ (iron from apples and rotisserie chickens)
5. $3x_0 + 3x_2 \geq 46$ (iron from cornichons and rotisserie chickens)
6. $3x_0 + x_1 + 3x_2 \geq 46$ (total iron from all sources)
7. $6x_0 + 6x_1 \geq 51$ (umami index from cornichons and apples)
8. $6x_0 + 6x_1 + 7x_2 \geq 43$ (total umami index from all sources)
9. $4x_0 - 8x_2 \geq 0$ (relationship between cornichons and rotisserie chickens)
10. $x_1 + 3x_2 \leq 50$ (iron limit from apples and rotisserie chickens)
11. $3x_0 + x_1 \leq 64$ (iron limit from cornichons and apples)
12. $6x_0 + 6x_1 \leq 144$ (umami index limit from cornichons and apples)
13. $6x_0 + 7x_2 \leq 100$ (umami index limit from cornichons and rotisserie chickens)

## 4: Specify the symbolic representation in JSON format
```json
{
'sym_variables': [('x0', 'cornichons'), ('x1', 'apples'), ('x2', 'rotisserie chickens')],
'objective_function': '9.55*x0 + 6.3*x1 + 2.65*x2',
'constraints': [
    '3*x0 + x1 + 3*x2 <= 143',
    '6*x0 + 6*x1 + 7*x2 <= 175',
    'x1 + 3*x2 >= 47',
    '3*x0 + 3*x2 >= 46',
    '3*x0 + x1 + 3*x2 >= 46',
    '6*x0 + 6*x1 >= 51',
    '6*x0 + 6*x1 + 7*x2 >= 43',
    '4*x0 - 8*x2 >= 0',
    'x1 + 3*x2 <= 50',
    '3*x0 + x1 <= 64',
    '6*x0 + 6*x1 <= 144',
    '6*x0 + 7*x2 <= 100'
]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name="cornichons", lb=0)
    x1 = model.addVar(name="apples", lb=0)
    x2 = model.addVar(name="rotisserie_chickens", lb=0, integrality=gurobi.GRB.INTEGER)

    # Set the objective function
    model.setObjective(9.55 * x0 + 6.3 * x1 + 2.65 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(3 * x0 + x1 + 3 * x2 <= 143)
    model.addConstr(6 * x0 + 6 * x1 + 7 * x2 <= 175)
    model.addConstr(x1 + 3 * x2 >= 47)
    model.addConstr(3 * x0 + 3 * x2 >= 46)
    model.addConstr(3 * x0 + x1 + 3 * x2 >= 46)
    model.addConstr(6 * x0 + 6 * x1 >= 51)
    model.addConstr(6 * x0 + 6 * x1 + 7 * x2 >= 43)
    model.addConstr(4 * x0 - 8 * x2 >= 0)
    model.addConstr(x1 + 3 * x2 <= 50)
    model.addConstr(3 * x0 + x1 <= 64)
    model.addConstr(6 * x0 + 6 * x1 <= 144)
    model.addConstr(6 * x0 + 7 * x2 <= 100)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("cornichons: ", x0.varValue)
        print("apples: ", x1.varValue)
        print("rotisserie_chickens: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```