To solve this optimization problem, we first need to define the variables, objective function, and constraints using Gurobi's Python API.

### Problem Definition

We have four variables:
- \(x_0\): bowls of instant ramen
- \(x_1\): granola bars
- \(x_2\): green beans
- \(x_3\): hamburgers

### Resources/Attributes

Given resources/attributes:
- \(r_0\): grams of protein
- \(r_1\): grams of carbohydrates

### Objective Function

Maximize: \(7.17x_0^2 + 7.28x_1^2 + 4.4x_1x_2 + 4.41x_2x_3\)

### Constraints

1. \(6x_0 + 15x_3 \geq 22\)
2. \(6x_0 + 2x_2 \geq 14\)
3. \(6^2x_0^2 + 16^2x_1^2 + 2^2x_2^2 \geq 21\)
4. \(6x_0 + 16x_1 + 15x_3 \geq 21\)
5. \(6^2x_0^2 + 16^2x_1^2 + 2^2x_2^2 \geq 18\)
6. \(6x_0 + 16x_1 + 15x_3 \geq 18\)
7. \(14x_0 + 16x_3 \geq 29\)
8. \(14x_0 + 4x_1 \geq 21\)
9. \(14x_0 + 4x_1 + 10x_2 \geq 23\)
10. \(2^2x_2^2 + 15^2x_3^2 \leq 87\)
11. \(6^2x_0^2 + 15^2x_3^2 \leq 74\)
12. \(16^2x_1^2 + 2^2x_2^2 \leq 66\)
13. \(6^2x_0^2 + 16^2x_1^2 \leq 95\)
14. \(6x_0 + 16x_1 + 2x_2 + 15x_3 \leq 95\)
15. \(14^2x_0^2 + 4^2x_1^2 \leq 93\)
16. \(14^2x_0^2 + 10^2x_2^2 \leq 110\)
17. \(4x_1 + 16x_3 \leq 100\)
18. \(4x_1 + 10x_2 \leq 139\)
19. \(14^2x_0^2 + 4^2x_1^2 + 10^2x_2^2 \leq 119\)
20. \(4^2x_1^2 + 10^2x_2^2 + 16^2x_3^2 \leq 117\)
21. \(14x_0 + 4x_1 + 16x_3 \leq 126\)
22. \(14x_0 + 4x_1 + 10x_2 + 16x_3 \leq 126\)

### Gurobi Code

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, name="bowls_of_instant_ramen")
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, name="granola_bars")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, name="green_beans")
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, name="hamburgers")

    # Objective function
    model.setObjective(7.17 * x0**2 + 7.28 * x1**2 + 4.4 * x1 * x2 + 4.41 * x2 * x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6 * x0 + 15 * x3 >= 22)
    model.addConstr(6 * x0 + 2 * x2 >= 14)
    model.addConstr(6**2 * x0**2 + 16**2 * x1**2 + 2**2 * x2**2 >= 21)
    model.addConstr(6 * x0 + 16 * x1 + 15 * x3 >= 21)
    model.addConstr(6**2 * x0**2 + 16**2 * x1**2 + 2**2 * x2**2 >= 18)
    model.addConstr(6 * x0 + 16 * x1 + 15 * x3 >= 18)
    model.addConstr(14 * x0 + 16 * x3 >= 29)
    model.addConstr(14 * x0 + 4 * x1 >= 21)
    model.addConstr(14 * x0 + 4 * x1 + 10 * x2 >= 23)
    model.addConstr(2**2 * x2**2 + 15**2 * x3**2 <= 87)
    model.addConstr(6**2 * x0**2 + 15**2 * x3**2 <= 74)
    model.addConstr(16**2 * x1**2 + 2**2 * x2**2 <= 66)
    model.addConstr(6**2 * x0**2 + 16**2 * x1**2 <= 95)
    model.addConstr(6 * x0 + 16 * x1 + 2 * x2 + 15 * x3 <= 95)
    model.addConstr(14**2 * x0**2 + 4**2 * x1**2 <= 93)
    model.addConstr(14**2 * x0**2 + 10**2 * x2**2 <= 110)
    model.addConstr(4 * x1 + 16 * x3 <= 100)
    model.addConstr(4 * x1 + 10 * x2 <= 139)
    model.addConstr(14**2 * x0**2 + 4**2 * x1**2 + 10**2 * x2**2 <= 119)
    model.addConstr(4**2 * x1**2 + 10**2 * x2**2 + 16**2 * x3**2 <= 117)
    model.addConstr(14 * x0 + 4 * x1 + 16 * x3 <= 126)
    model.addConstr(14 * x0 + 4 * x1 + 10 * x2 + 16 * x3 <= 126)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("bowls_of_instant_ramen: ", x0.varValue)
        print("granola_bars: ", x1.varValue)
        print("green_beans: ", x2.varValue)
        print("hamburgers: ", x3.varValue)
    else:
        print("No solution found")

solve_optimization_problem()
```