To solve the optimization problem described, we first need to understand and translate the given natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints.

Given:
- Variables: milligrams of vitamin E (let's denote this as `x1`) and milligrams of vitamin B9 (denoted as `x2`).
- Objective Function: Minimize `4.45*x1 + 1.29*x2`.
- Constraints:
  1. Cognitive performance index from vitamin E: `1*x1`.
  2. Muscle growth index from vitamin E: `2*x1`.
  3. Cognitive performance index from vitamin B9: `7*x2`.
  4. Muscle growth index from vitamin B9: `2*x2`.
  5. Total cognitive performance index >= 21: `x1 + 7*x2 >= 21`.
  6. Same as constraint 5, ensuring it's at least 21.
  7. Total muscle growth index >= 20: `2*x1 + 2*x2 >= 20`.
  8. Same as constraint 7, emphasizing it must be at least 20.
  9. `-3*x1 + 6*x2 >= 0`.
  10. Maximum total cognitive performance index <= 47: `x1 + 7*x2 <= 47`.
  11. Maximum total muscle growth index <= 28: `2*x1 + 2*x2 <= 28`.
  12. Vitamin E must be an integer.
  13. Vitamin B9 can be non-integer.

The symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'milligrams of vitamin E'), ('x2', 'milligrams of vitamin B9')],
  'objective_function': '4.45*x1 + 1.29*x2',
  'constraints': [
    'x1 + 7*x2 >= 21',
    '2*x1 + 2*x2 >= 20',
    '-3*x1 + 6*x2 >= 0',
    'x1 + 7*x2 <= 47',
    '2*x1 + 2*x2 <= 28'
  ]
}
```

Now, to express this problem in Gurobi Python code:

```python
from gurobipy import *

# Create a new model
model = Model("Vitamin_Optimization")

# Add variables
x1 = model.addVar(vtype=GRB.INTEGER, name="vitamin_e")
x2 = model.addVar(vtype=GRB.CONTINUOUS, name="vitamin_b9")

# Set the objective function
model.setObjective(4.45*x1 + 1.29*x2, GRB.MINIMIZE)

# Add constraints
model.addConstr(x1 + 7*x2 >= 21, "cognitive_performance_min")
model.addConstr(2*x1 + 2*x2 >= 20, "muscle_growth_min")
model.addConstr(-3*x1 + 6*x2 >= 0, "vitamin_balance")
model.addConstr(x1 + 7*x2 <= 47, "cognitive_performance_max")
model.addConstr(2*x1 + 2*x2 <= 28, "muscle_growth_max")

# Optimize the model
model.optimize()

# Print solution
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Vitamin E (mg): {x1.x}")
    print(f"Vitamin B9 (mg): {x2.x}")
else:
    print("No optimal solution found")
```