## Step 1: Define the symbolic representation of the variables
The variables are 'rotisserie chickens' and 'apples', 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 minimize is $8.8 \times \text{rotisserie chickens} + 7.52 \times \text{apples}$, which in symbolic terms is $8.8x_1 + 7.52x_2$.

## 3: Define the constraints in symbolic representation
1. $1x_1 + 12x_2 \geq 11$ (at least 11 grams of fat from both)
2. $4x_1 + 10x_2 \geq 11$ (at least $11 spent on both)
3. $10x_1 - 6x_2 \geq 0$ ( constraint involving rotisserie chickens and apples)
4. $1x_1 + 12x_2 \leq 43$ (no more than 43 grams of fat from both)
5. $4x_1 + 10x_2 \leq 55$ (no more than $55 spent on both)
6. $x_1 \geq 0$ and $x_1$ is an integer (non-fractional amount of rotisserie chickens)
7. $x_2 \geq 0$ (apples can be a fractional amount)

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'rotisserie chickens'), ('x2', 'apples')],
'objective_function': '8.8x1 + 7.52x2',
'constraints': [
    '1x1 + 12x2 >= 11',
    '4x1 + 10x2 >= 11',
    '10x1 - 6x2 >= 0',
    '1x1 + 12x2 <= 43',
    '4x1 + 10x2 <= 55',
    'x1 >= 0 and x1 is an integer',
    'x2 >= 0'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

# Define the model
model = gurobi.Model()

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

# Set the objective function
model.setObjective(8.8 * x1 + 7.52 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(1 * x1 + 12 * x2 >= 11, name="fat_constraint")
model.addConstr(4 * x1 + 10 * x2 >= 11, name="cost_constraint")
model.addConstr(10 * x1 - 6 * x2 >= 0, name="mix_constraint")
model.addConstr(1 * x1 + 12 * x2 <= 43, name="max_fat_constraint")
model.addConstr(4 * x1 + 10 * x2 <= 55, name="max_cost_constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Rotisserie chickens: {x1.varValue}")
    print(f"Apples: {x2.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```