## Step 1: Define the symbolic representation of the variables
The variables are 'peanutbutter sandwiches', 'cantaloupes', and 'rotisserie chickens'. Let's denote them 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 $4x_0 + 1x_1 + 8x_2$.

## Step 3: Define the constraints in symbolic notation
1. Healthiness rating constraints:
- $0.3x_0 + 0.35x_1 + 1.27x_2 \geq 10$ (total healthiness rating)
- However, we have more specific constraints:
- $0.35x_1 + 1.27x_2 \geq 10$ 
- $0.3x_0 + 0.35x_1 \geq 10$
- $0.3x_0 + 0.35x_1 + 1.27x_2 \geq 10$ (redundant with the total)

2. Iron constraints:
- $1.13x_0 + 0.09x_2 \geq 4$
- $1.13x_0 + 1.47x_1 \geq 7$
- $1.13x_0 + 1.47x_1 + 0.09x_2 \geq 4$ (and another identical constraint)

3. Other constraints:
- $-8x_0 + 4x_1 \geq 0$
- $1.47x_1 + 0.09x_2 \leq 23$

4. Bounds and integrality:
- $x_0$ is an integer
- $x_1$ is an integer
- $x_2$ is continuous

## Step 4: Provide the symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'peanutbutter sandwiches'), ('x1', 'cantaloupes'), ('x2', 'rotisserie chickens')],
'objective_function': '4*x0 + 1*x1 + 8*x2',
'constraints': [
    '0.35*x1 + 1.27*x2 >= 10',
    '0.3*x0 + 0.35*x1 >= 10',
    '0.3*x0 + 0.35*x1 + 1.27*x2 >= 10',
    '1.13*x0 + 0.09*x2 >= 4',
    '1.13*x0 + 1.47*x1 >= 7',
    '1.13*x0 + 1.47*x1 + 0.09*x2 >= 4',
    '-8*x0 + 4*x1 >= 0',
    '1.47*x1 + 0.09*x2 <= 23'
]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="peanutbutter_sandwiches", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="cantaloupes", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="rotisserie_chickens")

    # Objective function
    model.setObjective(4*x0 + x1 + 8*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(0.35*x1 + 1.27*x2 >= 10)
    model.addConstr(0.3*x0 + 0.35*x1 >= 10)
    model.addConstr(1.13*x0 + 0.09*x2 >= 4)
    model.addConstr(1.13*x0 + 1.47*x1 >= 7)
    model.addConstr(1.13*x0 + 1.47*x1 + 0.09*x2 >= 4)
    model.addConstr(-8*x0 + 4*x1 >= 0)
    model.addConstr(1.47*x1 + 0.09*x2 <= 23)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Peanutbutter sandwiches: {x0.varValue}")
        print(f"Cantaloupes: {x1.varValue}")
        print(f"Rotisserie chickens: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```