## Step 1: Define the symbolic representation of the variables
The variables are 'chicken breasts', 'hamburgers', and 'kiwis', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $2.97x_0^2 + 7.99x_0x_1 + 5.42x_0x_2 + 8.42x_1^2 + 5.13x_1x_2 + 9.59x_0 + 9.47x_1 + 1.94x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $x_0 \geq 0$ (no lower bound given, but assumed non-negative)
- $x_1$ is an integer
- $x_2$ is an integer
- $1x_0 + 9x_1 + 12x_2 \leq 386$ (calcium constraint)
- $24x_0 + 26x_1 + 26x_2 \leq 238$ (sourness index constraint)
- $x_0^2 + x_2^2 \geq 70$ (calcium from chicken breasts and kiwis)
- $x_1^2 + x_2^2 \geq 67$ (calcium from hamburgers and kiwis)
- $x_0 + x_1 \geq 88$ (calcium from chicken breasts and hamburgers)
- $x_0 + x_1 + x_2 \geq 88$ (calcium from all sources)
- $26x_1 + 26x_2 \geq 41$ (sourness index from hamburgers and kiwis)
- $24x_0 + 26x_1 \geq 60$ (sourness index from chicken breasts and hamburgers)
- $24x_0 + 26x_1 + 26x_2 \geq 60$ (sourness index from all sources)
- $-6x_0 + 5x_2 \geq 0$ (relationship between chicken breasts and kiwis)
- $9x_1^2 + 12x_2^2 \leq 383$ (calcium limit from hamburgers and kiwis squared)
- $x_0 + 12x_2 \leq 317$ (calcium limit from chicken breasts and kiwis)
- $x_0^2 + x_1^2 + x_2^2 \leq 355$ (calcium limit from all sources squared)
- $24x_0 + 26x_2 \leq 161$ (sourness index limit from chicken breasts and kiwis)
- $(24x_0)^2 + (26x_1)^2 + (26x_2)^2 \leq 107$ (sourness index limit from all sources squared)

## 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'chicken breasts'), ('x1', 'hamburgers'), ('x2', 'kiwis')],
    'objective_function': '2.97*x0^2 + 7.99*x0*x1 + 5.42*x0*x2 + 8.42*x1^2 + 5.13*x1*x2 + 9.59*x0 + 9.47*x1 + 1.94*x2',
    'constraints': [
        '1*x0 + 9*x1 + 12*x2 <= 386',
        '24*x0 + 26*x1 + 26*x2 <= 238',
        'x0^2 + x2^2 >= 70',
        'x1^2 + x2^2 >= 67',
        'x0 + x1 >= 88',
        'x0 + x1 + x2 >= 88',
        '26*x1 + 26*x2 >= 41',
        '24*x0 + 26*x1 >= 60',
        '24*x0 + 26*x1 + 26*x2 >= 60',
        '-6*x0 + 5*x2 >= 0',
        '9*x1^2 + 12*x2^2 <= 383',
        'x0 + 12*x2 <= 317',
        'x0^2 + x1^2 + x2^2 <= 355',
        '24*x0 + 26*x2 <= 161',
        '(24*x0)^2 + (26*x1)^2 + (26*x2)^2 <= 107'
    ]
}
```

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

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

    # Define variables
    x0 = model.addVar(lb=0, name="chicken_breasts")  # No lower bound given, assuming non-negative
    x1 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="hamburgers")
    x2 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="kiwis")

    # Objective function
    model.setObjective(2.97*x0**2 + 7.99*x0*x1 + 5.42*x0*x2 + 8.42*x1**2 + 5.13*x1*x2 + 9.59*x0 + 9.47*x1 + 1.94*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(1*x0 + 9*x1 + 12*x2 <= 386)
    model.addConstr(24*x0 + 26*x1 + 26*x2 <= 238)
    model.addConstr(x0**2 + x2**2 >= 70)
    model.addConstr(x1**2 + x2**2 >= 67)
    model.addConstr(x0 + x1 >= 88)
    model.addConstr(x0 + x1 + x2 >= 88)
    model.addConstr(26*x1 + 26*x2 >= 41)
    model.addConstr(24*x0 + 26*x1 >= 60)
    model.addConstr(24*x0 + 26*x1 + 26*x2 >= 60)
    model.addConstr(-6*x0 + 5*x2 >= 0)
    model.addConstr(9*x1**2 + 12*x2**2 <= 383)
    model.addConstr(x0 + 12*x2 <= 317)
    model.addConstr(x0**2 + x1**2 + x2**2 <= 355)
    model.addConstr(24*x0 + 26*x2 <= 161)
    model.addConstr((24*x0)**2 + (26*x1)**2 + (26*x2)**2 <= 107)

    # Solve the model
    model.optimize()

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

solve_optimization_problem()
```