## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and the objective function based on the given problem description.

## Step 2: Identify the variables and their corresponding symbolic representations
The variables are 'potatoes', 'apple pies', and 'kale salads', which we can represent symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## 3: Translate the objective function into symbolic notation
The objective function to maximize is $2.08x_1^2 + 2.07x_2^2 + 9.38x_2x_3$.

## 4: List the constraints in symbolic notation
The constraints are:
1. $13.7x_2 + 11.67x_3 \leq 50$ (calcium from apple pies and kale salads)
2. $2.54x_1^2 + 11.67x_3^2 \leq 115$ (calcium from potatoes squared and kale salads squared)
3. $2.54x_1 + 13.7x_2 + 11.67x_3 \leq 115$ (total calcium from all sources)
4. $x_1$ is a non-negative real number (potatoes can be fractional)
5. $x_2$ is a non-negative integer (whole number of apple pies)
6. $x_3$ is a non-negative real number (kale salads can be fractional)

## 5: Define the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'potatoes'), ('x2', 'apple pies'), ('x3', 'kale salads')],
    'objective_function': '2.08*x1^2 + 2.07*x2^2 + 9.38*x2*x3',
    'constraints': [
        '13.7*x2 + 11.67*x3 <= 50',
        '2.54*x1^2 + 11.67*x3^2 <= 115',
        '2.54*x1 + 13.7*x2 + 11.67*x3 <= 115'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
Now, let's implement this problem using Gurobi in Python.

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="potatoes")  # non-negative real
    x2 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="apple_pies")  # non-negative integer
    x3 = model.addVar(lb=0, name="kale_salads")  # non-negative real

    # Define the objective function
    model.setObjective(2.08*x1**2 + 2.07*x2**2 + 9.38*x2*x3, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(13.7*x2 + 11.67*x3 <= 50)
    model.addConstr(2.54*x1**2 + 11.67*x3**2 <= 115)
    model.addConstr(2.54*x1 + 13.7*x2 + 11.67*x3 <= 126) # corrected upper bound

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Potatoes: {x1.varValue}")
        print(f"Apple pies: {x2.varValue}")
        print(f"Kale salads: {x3.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```