## Problem Description and Formulation

The problem is an optimization problem with two variables: 'protein bars' and 'strawberries'. The objective function to be maximized is \(9 \times (\text{protein bars})^2 + 9 \times \text{protein bars} \times \text{strawberries}\).

The problem has several constraints:
1. The tastiness rating of protein bars is 13.
2. There are 8 grams of protein in protein bars.
3. Protein bars each have a umami index of 3.
4. Strawberries have a tastiness rating of 14 each.
5. There are 12 grams of protein in strawberries.
6. Strawberries have a umami index of 5.
7. The total combined tastiness rating from protein bars squared and strawberries squared should be no less than 24.
8. The total combined grams of protein from protein bars squared and strawberries squared has to be 12 at minimum.
9. The total combined umami index from protein bars and strawberries should be no less than 32.
10. \(7 \times \text{protein bars} - 10 \times \text{strawberries} \geq 0\).
11. The total combined tastiness rating from protein bars plus strawberries must be 41 or less.
12. The total combined grams of protein from protein bars plus strawberries should be 36 or less.
13. The total combined umami index from protein bars squared and strawberries squared should be less than or equal to 40.
14. The total combined umami index from protein bars and strawberries has to be 40 at maximum.
15. Protein bars are restricted to an integer number.
16. Strawberries do not have to be a whole number.

## Gurobi Code Formulation

```python
import gurobipy as gp
from gurobipy import GRB

# Create a new model
model = gp.Model("protein_bars_strawberries")

# Define variables
protein_bars = model.addVar(vtype=GRB.INTEGER, name="protein_bars")
strawberries = model.addVar(vtype=GRB.CONTINUOUS, name="strawberries")

# Objective function
model.setObjective(9 * protein_bars ** 2 + 9 * protein_bars * strawberries, GRB.MAXIMIZE)

# Constraints
model.addConstr(protein_bars >= 0, name="protein_bars_non_negative")
model.addConstr(strawberries >= 0, name="strawberries_non_negative")

# Constraint 7: Total combined tastiness rating squared
model.addConstr(13 ** 2 * protein_bars ** 2 + 14 ** 2 * strawberries ** 2 >= 24, name="tastiness_rating_squared")

# Constraint 8: Total combined grams of protein squared
model.addConstr(8 ** 2 * protein_bars ** 2 + 12 ** 2 * strawberries ** 2 >= 12, name="grams_protein_squared")

# Constraint 9: Total combined umami index
model.addConstr(3 * protein_bars + 5 * strawberries >= 32, name="umami_index")

# Constraint 10: 7 * protein bars - 10 * strawberries >= 0
model.addConstr(7 * protein_bars - 10 * strawberries >= 0, name="protein_bars_strawberries_ratio")

# Constraint 11 & 12: Total combined tastiness rating
model.addConstr(13 * protein_bars + 14 * strawberries <= 41, name="total_tastiness_rating")

# Constraint 13 & 14: Total combined grams of protein
model.addConstr(8 * protein_bars + 12 * strawberries <= 36, name="total_grams_protein")

# Constraint 15: Total combined umami index squared
model.addConstr(3 ** 2 * protein_bars ** 2 + 5 ** 2 * strawberries ** 2 <= 40, name="umami_index_squared")

# Constraint 16: Total combined umami index
model.addConstr(3 * protein_bars + 5 * strawberries <= 40, name="total_umami_index")

# Solve the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Protein Bars: {protein_bars.varValue}")
    print(f"Strawberries: {strawberries.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("The model is infeasible.")
```