## Step 1: Define the symbolic representation of the variables
The variables are ['potatoes', 'cherry pies', 'rotisserie chickens', 'cantaloupes'], which can be represented symbolically as ['x1', 'x2', 'x3', 'x4'].

## Step 2: Create the symbolic representation of the problem
The symbolic representation of the variables is:
- x1: potatoes
- x2: cherry pies
- x3: rotisserie chickens
- x4: cantaloupes

## Step 3: Formulate the objective function using symbolic variables
The objective function to maximize is: $6x1^2 + 7x1x3 + 5x2^2 + 4x2x3 + 2x3^2 + 6x3x4 + 5x4^2 + x1$.

## 4: Define the constraints using symbolic variables
The constraints are:
- $13x1 + 10x2 + 11x3 + 2x4 \leq 61$ (total carbohydrates constraint, but we have specific constraints below that make this redundant)
- $13x1 + 2x4 \leq 21$ (carbohydrates from potatoes and cantaloupes)
- $13x1 + 10x2 \leq 46$ (carbohydrates from potatoes and cherry pies)
- $13x1 + 10x2 + 11x3 + 2x4 \leq 46$ (carbohydrates from all sources, but note this is more restrictive than needed given other constraints)
- $x1, x2, x3, x4$ are integers (whole numbers)

## 5: Correct and simplify constraints based on the problem statement
Given:
- $13x1 \leq 13$ (implicit from potatoes alone, but we consider $13x1 + 2x4 \leq 21$)
- $10x2 \leq 10$ (implicit from cherry pies alone, but we consider $13x1 + 10x2 \leq 46$)
- $11x3$ and $2x4$ have implicit limits from the total

## 6: Write down the problem in a suitable format for Gurobi
The problem can be described as:
```json
{
'sym_variables': [('x1', 'potatoes'), ('x2', 'cherry pies'), ('x3', 'rotisserie chickens'), ('x4', 'cantaloupes')],
'objective_function': '6*x1^2 + 7*x1*x3 + 5*x2^2 + 4*x2*x3 + 2*x3^2 + 6*x3*x4 + 5*x4^2 + x1',
'constraints': [
'13*x1 + 2*x4 <= 21',
'13*x1 + 10*x2 <= 46',
'13*x1 + 10*x2 + 11*x3 + 2*x4 <= 46',
'x1 >= 0', 'x2 >= 0', 'x3 >= 0', 'x4 >= 0',
'x1 % 1 == 0', 'x2 % 1 == 0', 'x3 % 1 == 0', 'x4 % 1 == 0'
]
}
```

## 7: Convert the problem into Gurobi Python code
```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define variables
x1 = m.addVar(name='potatoes', vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name='cherry_pies', vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name='rotisserie_chickens', vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name='cantaloupes', vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(6*x1**2 + 7*x1*x3 + 5*x2**2 + 4*x2*x3 + 2*x3**2 + 6*x3*x4 + 5*x4**2 + x1, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(13*x1 + 2*x4 <= 21)
m.addConstr(13*x1 + 10*x2 <= 46)
m.addConstr(13*x1 + 10*x2 + 11*x3 + 2*x4 <= 46)

# Optimize
m.optimize()

# Print solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Potatoes: ', x1.varValue)
    print('Cherry Pies: ', x2.varValue)
    print('Rotisserie Chickens: ', x3.varValue)
    print('Cantaloupes: ', x4.varValue)
else:
    print('No optimal solution found')
```