## Step 1: Define the symbolic representation of the variables
The variables are 'fruit salads' and 'potatoes', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $8.83x_1^2 + 6.48x_1x_2 + 3.67x_1 + 6.4x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $12x_1 + 8x_2 \geq 25$ (at least 25 grams of fat)
- $8x_1^2 + x_2^2 \geq 52$ (at least 52 milligrams of iron)
- $x_1^2 - 10x_2^2 \geq 0$
- $12^2x_1^2 + 8^2x_2^2 \leq 63^2$ (at most 63 grams of fat from squares)
- $12x_1 + 8x_2 \leq 63$ (at most 63 grams of fat)
- $8x_1 + 15x_2 \leq 141$ (at most 141 milligrams of iron)
- $8x_1 + 15x_2 \leq 141$ is redundant with the previous constraint, so we consider $8x_1 + 15x_2 \leq 141$ and $8x_1 + 15x_2 \geq 0$ implicitly as $x_1, x_2 \geq 0$ but $x_2$ is an integer.

## 4: Specify variable bounds and types
- $x_1$ is a continuous variable
- $x_2$ is an integer variable

## 5: Formulate the problem in Gurobi
To solve this problem using Gurobi, we will use the Gurobi Python API.

## 6: Write the Gurobi code
```python
import gurobi as gp

# Create a new model
m = gp.Model()

# Define the variables
x1 = m.addVar(lb=0, name="fruit_salads")  # continuous
x2 = m.addVar(lb=0, type=gp.GRB.INTEGER, name="potatoes")  # integer

# Define the objective function
m.setObjective(8.83*x1**2 + 6.48*x1*x2 + 3.67*x1 + 6.4*x2, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(12*x1 + 8*x2 >= 25, name="fat_constraint")
m.addConstr(8*x1**2 + x2**2 >= 52, name="iron_constraint")
m.addConstr(x1**2 - 10*x2**2 >= 0, name="ratio_constraint")
m.addConstr(144*x1**2 + 64*x2**2 <= 3969, name="fat_square_constraint")
m.addConstr(12*x1 + 8*x2 <= 63, name="fat_linear_constraint")
m.addConstr(8*x1 + 15*x2 <= 141, name="iron_linear_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Fruit Salads: ", x1.varValue)
    print("Potatoes: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic Representation
```json
{
    'sym_variables': [('x1', 'fruit salads'), ('x2', 'potatoes')],
    'objective_function': '8.83*x1^2 + 6.48*x1*x2 + 3.67*x1 + 6.4*x2',
    'constraints': [
        '12*x1 + 8*x2 >= 25',
        '8*x1^2 + x2^2 >= 52',
        'x1^2 - 10*x2^2 >= 0',
        '144*x1^2 + 64*x2^2 <= 3969',
        '12*x1 + 8*x2 <= 63',
        '8*x1 + 15*x2 <= 141'
    ]
}
```