## Problem Description and Formulation

The problem requires maximizing an objective function subject to several constraints. The objective function is:

\[ 6.51 \times \text{potatoes}^2 + 6.3 \times \text{potatoes} \times \text{rotisserie chickens} + 8.57 \times \text{rotisserie chickens}^2 + 3.48 \times \text{rotisserie chickens} \times \text{corn cobs} + 7.18 \times \text{corn cobs}^2 + 4.64 \times \text{rotisserie chickens} + 3.49 \times \text{corn cobs} \]

Subject to the following constraints:

1. The healthiness rating of potatoes is 5.32.
2. The healthiness rating of rotisserie chickens is 5.14.
3. The healthiness rating of corn cobs is 0.57.
4. \(-1 \times \text{rotisserie chickens} + 10 \times \text{corn cobs} \geq 0\).
5. The total combined healthiness rating from potatoes and corn cobs must be less than or equal to 47.
6. The total combined healthiness rating from rotisserie chickens squared and corn cobs squared must be less than or equal to 67.
7. The total combined healthiness rating from potatoes squared and rotisserie chickens squared must be less than or equal to 74.
8. The total combined healthiness rating from potatoes, rotisserie chickens, and corn cobs must be less than or equal to 74.
9. Potatoes can be a non-integer amount.
10. Rotisserie chickens must be an integer.
11. Corn cobs can be a fractional number.

## Gurobi Code Formulation

```python
import gurobipy as gp

# Define the model
model = gp.Model("optimization_problem")

# Define the variables
potatoes = model.addVar(lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, name="potatoes")
rotisserie_chickens = model.addVar(lb=0, ub=gp.GRB.INFINITY, type=gp.GRB.INTEGER, name="rotisserie_chickens")
corn_cobs = model.addVar(lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, name="corn_cobs")

# Objective function
model.setObjective(6.51 * potatoes**2 + 6.3 * potatoes * rotisserie_chickens + 8.57 * rotisserie_chickens**2 + 
                   3.48 * rotisserie_chickens * corn_cobs + 7.18 * corn_cobs**2 + 4.64 * rotisserie_chickens + 
                   3.49 * corn_cobs, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(potatoes == 5.32, name="healthiness_rating_potatoes")
model.addConstr(rotisserie_chickens == 5.14, name="healthiness_rating_rotisserie_chickens")
model.addConstr(corn_cobs == 0.57, name="healthiness_rating_corn_cobs")

model.addConstr(-rotisserie_chickens + 10 * corn_cobs >= 0, name="rotisserie_chickens_corn_cobs_constraint")

# Healthiness rating constraints
model.addConstr(5.32 * potatoes + 0.57 * corn_cobs <= 47, name="potatoes_corn_cobs_healthiness")
model.addConstr(5.14**2 * rotisserie_chickens**2 + 0.57**2 * corn_cobs**2 <= 67, name="rotisserie_chickens_corn_cobs_healthiness_squared")
model.addConstr(5.32**2 * potatoes**2 + 5.14**2 * rotisserie_chickens**2 <= 74, name="potatoes_rotisserie_chickens_healthiness_squared")
model.addConstr(5.32 * potatoes + 5.14 * rotisserie_chickens + 0.57 * corn_cobs <= 74, name="total_healthiness")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Potatoes: {potatoes.varValue}")
    print(f"Rotisserie Chickens: {rotisserie_chickens.varValue}")
    print(f"Corn Cobs: {corn_cobs.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("The model is infeasible or unbounded.")
```