## Problem Description and Formulation

The problem is an optimization problem with integer variables. The goal is to maximize an objective function subject to several constraints related to the amount of carbohydrates from different food items.

### Variables

- `potatoes`
- `cherry pies`
- `rotisserie chickens`
- `cantaloupes`

### Objective Function

Maximize: 
\[ 6 \times \text{potatoes}^2 + 7 \times \text{potatoes} \times \text{rotisserie chickens} + 5 \times \text{cherry pies}^2 + 4 \times \text{cherry pies} \times \text{rotisserie chickens} + 2 \times \text{rotisserie chickens}^2 + 6 \times \text{rotisserie chickens} \times \text{cantaloupes} + 5 \times \text{cantaloupes}^2 + 1 \times \text{potatoes} \]

### Constraints

1. Carbohydrates in potatoes: \(13 \times \text{potatoes}\)
2. Carbohydrates in cherry pies: \(10 \times \text{cherry pies}\)
3. Carbohydrates in rotisserie chickens: \(11 \times \text{rotisserie chickens}\)
4. Carbohydrates in cantaloupes: \(2 \times \text{cantaloupes}\)
5. Total carbohydrates from potatoes and cantaloupes: \(13 \times \text{potatoes} + 2 \times \text{cantaloupes} \leq 21\)
6. Total carbohydrates from potatoes and cherry pies: \(13 \times \text{potatoes} + 10 \times \text{cherry pies} \leq 46\)
7. Total carbohydrates from all items: \(13 \times \text{potatoes} + 10 \times \text{cherry pies} + 11 \times \text{rotisserie chickens} + 2 \times \text{cantaloupes} \leq 46\)
8. Variables must be integers.

## Gurobi Code

```python
import gurobi

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

    # Define variables
    potatoes = model.addVar(name="potatoes", vtype=gurobi.GRB.INTEGER)
    cherry_pies = model.addVar(name="cherry_pies", vtype=gurobi.GRB.INTEGER)
    rotisserie_chickens = model.addVar(name="rotisserie_chickens", vtype=gurobi.GRB.INTEGER)
    cantaloupes = model.addVar(name="cantaloupes", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(6 * potatoes**2 + 7 * potatoes * rotisserie_chickens + 5 * cherry_pies**2 + 
                       4 * cherry_pies * rotisserie_chickens + 2 * rotisserie_chickens**2 + 
                       6 * rotisserie_chickens * cantaloupes + 5 * cantaloupes**2 + potatoes, 
                       gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(13 * potatoes + 2 * cantaloupes <= 21)
    model.addConstr(13 * potatoes + 10 * cherry_pies <= 46)
    model.addConstr(13 * potatoes + 10 * cherry_pies + 11 * rotisserie_chickens + 2 * cantaloupes <= 46)

    # Non-negativity constraints (implicit for integer variables)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Potatoes: {potatoes.varValue}")
        print(f"Cherry Pies: {cherry_pies.varValue}")
        print(f"Rotisserie Chickens: {rotisserie_chickens.varValue}")
        print(f"Cantaloupes: {cantaloupes.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("The model is infeasible or unbounded.")

solve_optimization_problem()
```