To solve the given optimization problem using Gurobi, we first need to understand and possibly simplify or clarify the constraints and objective function provided.

The objective is to maximize \(2x_0 + 4x_1\), where:
- \(x_0\) represents the number of protein bars,
- \(x_1\) represents the quantity of strawberries.

Given constraints:
1. Sourness index: \(14x_0 + 3x_1 \geq 6\) and \(14x_0 + 3x_1 \leq 17\).
2. Iron: \(2x_0 + 14x_1 \geq 23\) and \(2x_0 + 14x_1 \leq 39\).
3. Calcium: \(4x_0 + 12x_1 \geq 23\) and \(4x_0 + 12x_1 \leq 44\).
4. Protein: \(11x_0 + 3x_1 \geq 5\) and \(11x_0 + 3x_1 \leq 26\).
5. Additional constraint: \(4x_0 - 9x_1 \geq 0\).

Since the problem involves both integer (\(x_0\)) and continuous (\(x_1\)) variables, we'll use a Mixed-Integer Linear Programming (MILP) model.

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the variables
x0 = m.addVar(vtype=GRB.INTEGER, name="protein_bars")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="strawberries", lb=0)

# Objective function: Maximize 2*x0 + 4*x1
m.setObjective(2*x0 + 4*x1, GRB.MAXIMIZE)

# Constraints
# Sourness index constraints
m.addConstr(14*x0 + 3*x1 >= 6, name="sourness_index_min")
m.addConstr(14*x0 + 3*x1 <= 17, name="sourness_index_max")

# Iron constraints
m.addConstr(2*x0 + 14*x1 >= 23, name="iron_min")
m.addConstr(2*x0 + 14*x1 <= 39, name="iron_max")

# Calcium constraints
m.addConstr(4*x0 + 12*x1 >= 23, name="calcium_min")
m.addConstr(4*x0 + 12*x1 <= 44, name="calcium_max")

# Protein constraints
m.addConstr(11*x0 + 3*x1 >= 5, name="protein_min")
m.addConstr(11*x0 + 3*x1 <= 26, name="protein_max")

# Additional constraint
m.addConstr(4*x0 - 9*x1 >= 0, name="additional_constraint")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Protein bars: {x0.x}")
    print(f"Strawberries: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```