To solve the given optimization problem using Gurobi, we first need to understand and translate the natural language description into mathematical expressions that can be used in the code. The objective function is to minimize \(4.45 \times \text{milligrams of vitamin E} + 1.29 \times \text{milligrams of vitamin B9}\).

The constraints are as follows:
- Cognitive performance index from milligrams of vitamin E: 1
- Muscle growth index from milligrams of vitamin E: 2
- Cognitive performance index from milligrams of vitamin B9: 7
- Muscle growth index from milligrams of vitamin B9: 2
- Total cognitive performance index must be at least 21.
- Total muscle growth index must be at least 20.
- \(-3 \times \text{milligrams of vitamin E} + 6 \times \text{milligrams of vitamin B9} \geq 0\).
- Total cognitive performance index must not exceed 47.
- Total muscle growth index must not exceed 28.
- Milligrams of vitamin E must be an integer.
- Milligrams of vitamin B9 can be a non-integer.

Given the problem description, let's assign variables and formulate the constraints:
- Let \(x_0\) represent milligrams of vitamin E.
- Let \(x_1\) represent milligrams of vitamin B9.

The objective function to minimize is: \(4.45x_0 + 1.29x_1\).

Constraints based on the problem description:
1. Cognitive performance index constraint: \(1x_0 + 7x_1 \geq 21\)
2. Muscle growth index constraint: \(2x_0 + 2x_1 \geq 20\)
3. Additional linear constraint: \(-3x_0 + 6x_1 \geq 0\)
4. Upper bound on cognitive performance index: \(1x_0 + 7x_1 \leq 47\)
5. Upper bound on muscle growth index: \(2x_0 + 2x_1 \leq 28\)

Now, let's write the Gurobi code for this problem:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_vitamin_E")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B9")

# Set the objective function
m.setObjective(4.45*x0 + 1.29*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(1*x0 + 7*x1 >= 21, name="cognitive_performance_index_lower_bound")
m.addConstr(2*x0 + 2*x1 >= 20, name="muscle_growth_index_lower_bound")
m.addConstr(-3*x0 + 6*x1 >= 0, name="additional_linear_constraint")
m.addConstr(1*x0 + 7*x1 <= 47, name="cognitive_performance_index_upper_bound")
m.addConstr(2*x0 + 2*x1 <= 28, name="muscle_growth_index_upper_bound")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Milligrams of Vitamin E: {x0.x}")
    print(f"Milligrams of Vitamin B9: {x1.x}")
else:
    print("No optimal solution found. The model is either infeasible or unbounded.")
```