## Problem Description and Formulation

The problem is an optimization problem where we need to maximize a given objective function subject to several constraints. The variables are `lemons`, `potatoes`, `ravioli`, and `black beans`, and the constraints involve the amount of carbohydrates from each of these items.

## Objective Function

The objective function to maximize is:
\[ 7.44 \times \text{lemons}^2 + 5.02 \times \text{lemons} \times \text{potatoes} + 1.88 \times \text{lemons} \times \text{ravioli} + 2.78 \times \text{potatoes} + 7.87 \times \text{ravioli} + 8.79 \times \text{black beans} \]

## Constraints

1. Carbohydrates from each item:
   - Lemons: 11 grams
   - Potatoes: 20 grams
   - Ravioli: 15 grams
   - Black beans: 4 grams

2. At least 29 grams of carbohydrates must come from potatoes squared plus ravioli squared:
   \[ 20^2 \times \text{potatoes}^2 + 15^2 \times \text{ravioli}^2 \geq 29 \]
   Simplifying:
   \[ 400 \times \text{potatoes}^2 + 225 \times \text{ravioli}^2 \geq 29 \]

3. At least 37 grams of carbohydrates from lemons and ravioli:
   \[ 11 \times \text{lemons} + 15 \times \text{ravioli} \geq 37 \]

4. At most 86 grams of carbohydrates from ravioli and black beans:
   \[ 15 \times \text{ravioli} + 4 \times \text{black beans} \leq 86 \]

5. At most 218 grams of carbohydrates from potatoes and black beans:
   \[ 20 \times \text{potatoes} + 4 \times \text{black beans} \leq 218 \]

6. At most 185 grams of carbohydrates from lemons squared plus potatoes squared:
   \[ 11^2 \times \text{lemons}^2 + 20^2 \times \text{potatoes}^2 \leq 185 \]
   Simplifying:
   \[ 121 \times \text{lemons}^2 + 400 \times \text{potatoes}^2 \leq 185 \]

7. Total carbohydrates from all items at most 185 grams:
   \[ 11 \times \text{lemons} + 20 \times \text{potatoes} + 15 \times \text{ravioli} + 4 \times \text{black beans} \leq 185 \]

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    lemons = model.addVar(lb=0, name="lemons", vtype=gurobi.GRB.CONTINUOUS)
    potatoes = model.addVar(lb=0, name="potatoes", vtype=gurobi.GRB.CONTINUOUS)
    ravioli = model.addVar(lb=0, name="ravioli", vtype=gurobi.GRB.CONTINUOUS)
    black_beans = model.addVar(lb=0, name="black_beans", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(7.44 * lemons**2 + 5.02 * lemons * potatoes + 1.88 * lemons * ravioli +
                       2.78 * potatoes + 7.87 * ravioli + 8.79 * black_beans, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(400 * potatoes**2 + 225 * ravioli**2 >= 29, name="potatoes_ravioli_squared")
    model.addConstr(11 * lemons + 15 * ravioli >= 37, name="lemons_ravioli_carb")
    model.addConstr(15 * ravioli + 4 * black_beans <= 86, name="ravioli_black_beans_carb")
    model.addConstr(20 * potatoes + 4 * black_beans <= 218, name="potatoes_black_beans_carb")
    model.addConstr(121 * lemons**2 + 400 * potatoes**2 <= 185, name="lemons_potatoes_squared_carb")
    model.addConstr(11 * lemons + 20 * potatoes + 15 * ravioli + 4 * black_beans <= 185, name="total_carb")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Lemons: {lemons.varValue}")
        print(f"Potatoes: {potatoes.varValue}")
        print(f"Ravioli: {ravioli.varValue}")
        print(f"Black Beans: {black_beans.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```