## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_1$ represents 'milligrams of vitamin B3'
- $x_2$ represents 'milligrams of vitamin D'
- $x_3$ represents 'milligrams of vitamin B4'
- $x_4$ represents 'milligrams of vitamin C'

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $4x_1 + x_2 + 6x_3 + 2x_4$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $6x_1 \geq 6$ (cardiovascular support index of $x_1$)
- $3x_2 \geq 3$ (cardiovascular support index of $x_2$)
- $5x_3 \geq 5$ (cardiovascular support index of $x_3$)
- $1x_4 \geq 1$ (cardiovascular support index of $x_4$)
- $6x_1 + 3x_2 \geq 21$
- $5x_3 + 1x_4 \geq 17$
- $3x_2 + 1x_4 \geq 31$
- $3x_2 + 5x_3 \geq 24$
- $6x_1 + 3x_2 + 1x_4 \geq 23$
- $6x_1 + 3x_2 + 5x_3 + 1x_4 \geq 23$
- $x_2 - 2x_3 \geq 0$

## 4: Consider the bounds and types of variables
All variables are non-negative and can take non-integer values.

## 5: Write down the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin B3'), 
        ('x2', 'milligrams of vitamin D'), 
        ('x3', 'milligrams of vitamin B4'), 
        ('x4', 'milligrams of vitamin C')
    ], 
    'objective_function': '4*x1 + x2 + 6*x3 + 2*x4', 
    'constraints': [
        '6*x1 >= 6', 
        '3*x2 >= 3', 
        '5*x3 >= 5', 
        'x4 >= 1', 
        '6*x1 + 3*x2 >= 21', 
        '5*x3 + x4 >= 17', 
        '3*x2 + x4 >= 31', 
        '3*x2 + 5*x3 >= 24', 
        '6*x1 + 3*x2 + x4 >= 23', 
        '6*x1 + 3*x2 + 5*x3 + x4 >= 23', 
        'x2 - 2*x3 >= 0'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='x1', lb=0)  # milligrams of vitamin B3
    x2 = model.addVar(name='x2', lb=0)  # milligrams of vitamin D
    x3 = model.addVar(name='x3', lb=0)  # milligrams of vitamin B4
    x4 = model.addVar(name='x4', lb=0)  # milligrams of vitamin C

    # Objective function: minimize 4*x1 + x2 + 6*x3 + 2*x4
    model.setObjective(4*x1 + x2 + 6*x3 + 2*x4, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(6*x1 >= 6)
    model.addConstr(3*x2 >= 3)
    model.addConstr(5*x3 >= 5)
    model.addConstr(x4 >= 1)
    model.addConstr(6*x1 + 3*x2 >= 21)
    model.addConstr(5*x3 + x4 >= 17)
    model.addConstr(3*x2 + x4 >= 31)
    model.addConstr(3*x2 + 5*x3 >= 24)
    model.addConstr(6*x1 + 3*x2 + x4 >= 23)
    model.addConstr(6*x1 + 3*x2 + 5*x3 + x4 >= 23)
    model.addConstr(x2 - 2*x3 >= 0)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Optimal solution found.')
        print(f'milligrams of vitamin B3: {x1.varValue}')
        print(f'milligrams of vitamin D: {x2.varValue}')
        print(f'milligrams of vitamin B4: {x3.varValue}')
        print(f'milligrams of vitamin C: {x4.varValue}')
        print(f'Objective: {model.objVal}')
    else:
        print('No optimal solution found.')

optimize_vitamins()
```