## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of vitamin D', 'milligrams of vitamin B4', and 'milligrams of vitamin B12'. Let's denote them as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_0$ for 'milligrams of vitamin D'
- $x_1$ for 'milligrams of vitamin B4'
- $x_2$ for 'milligrams of vitamin B12'

## 3: Define the objective function in symbolic notation
The objective function to maximize is $4x_0^2 + 7x_0x_1 + 5x_1x_2 + 9x_0 + 6x_2$.

## 4: Define the constraints in symbolic notation
The constraints are:
- $8x_0 + 6x_1 \geq 4$
- $8x_0 + 6x_1 + 4x_2 \geq 5$
- $8x_0 + 4x_2 \leq 27$
- $8x_0 + 6x_1 \leq 17$
- $6x_1 + 4x_2 \leq 21$
- $8x_0 + 6x_1 + 4x_2 \leq 21$
- $3x_0 + 2x_1 \leq 15$
- $3x_0 + 7x_2 \leq 22$
- $3x_0 + 2x_1 + 7x_2 \leq 22$
- $x_0$ is a real number (no restriction, but implied by Gurobi's continuous variable)
- $x_1$ is an integer
- $x_2$ is an integer

## 5: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin D'), 
        ('x1', 'milligrams of vitamin B4'), 
        ('x2', 'milligrams of vitamin B12')
    ], 
    'objective_function': '4*x0^2 + 7*x0*x1 + 5*x1*x2 + 9*x0 + 6*x2', 
    'constraints': [
        '8*x0 + 6*x1 >= 4',
        '8*x0 + 6*x1 + 4*x2 >= 5',
        '8*x0 + 4*x2 <= 27',
        '8*x0 + 6*x1 <= 17',
        '6*x1 + 4*x2 <= 21',
        '8*x0 + 6*x1 + 4*x2 <= 21',
        '3*x0 + 2*x1 <= 15',
        '3*x0 + 7*x2 <= 22',
        '3*x0 + 2*x1 + 7*x2 <= 22'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x0")  # milligrams of vitamin D
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, vtype=gurobi.GRB.INTEGER, name="x1")  # milligrams of vitamin B4
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, vtype=gurobi.GRB.INTEGER, name="x2")  # milligrams of vitamin B12

    # Define the objective function
    model.setObjective(4*x0**2 + 7*x0*x1 + 5*x1*x2 + 9*x0 + 6*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(8*x0 + 6*x1 >= 4, name="c1")
    model.addConstr(8*x0 + 6*x1 + 4*x2 >= 5, name="c2")
    model.addConstr(8*x0 + 4*x2 <= 27, name="c3")
    model.addConstr(8*x0 + 6*x1 <= 17, name="c4")
    model.addConstr(6*x1 + 4*x2 <= 21, name="c5")
    model.addConstr(8*x0 + 6*x1 + 4*x2 <= 21, name="c6")
    model.addConstr(3*x0 + 2*x1 <= 15, name="c7")
    model.addConstr(3*x0 + 7*x2 <= 22, name="c8")
    model.addConstr(3*x0 + 2*x1 + 7*x2 <= 22, name="c9")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin D: {x0.varValue}")
        print(f"Milligrams of vitamin B4: {x1.varValue}")
        print(f"Milligrams of vitamin B12: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_vitamins()
```