## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin K', 'milligrams of vitamin B3', 'milligrams of vitamin E', 'milligrams of vitamin B12']. Let's denote them as $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_1$ for 'milligrams of vitamin K'
- $x_2$ for 'milligrams of vitamin B3'
- $x_3$ for 'milligrams of vitamin E'
- $x_4$ for 'milligrams of vitamin B12'

## 3: Define the objective function in symbolic notation
The objective function to minimize is $5x_1 + 1x_2 + 9x_3 + 1x_4$.

## 4: List the constraints in symbolic notation
The constraints are:
1. $1x_1 + 20x_2 \geq 91$
2. $20x_2 + 12x_3 \geq 49$
3. $1x_1 + 16x_4 \geq 82$
4. $20x_2 + 16x_4 \geq 69$
5. $1x_1 + 20x_2 + 12x_3 + 16x_4 \geq 69$
6. $1x_2 - 5x_4 \geq 0$
7. $4x_1 - 4x_4 \geq 0$
8. $9x_1 - 7x_3 + 7x_4 \geq 0$
9. $1x_1 + 16x_4 \leq 147$
10. $1x_1 + 20x_2 \leq 275$
11. $12x_3 + 16x_4 \leq 378$
12. $1x_1 + 20x_2 + 12x_3 \leq 228$

## 5: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin K'), 
        ('x2', 'milligrams of vitamin B3'), 
        ('x3', 'milligrams of vitamin E'), 
        ('x4', 'milligrams of vitamin B12')
    ], 
    'objective_function': '5*x1 + 1*x2 + 9*x3 + 1*x4', 
    'constraints': [
        '1*x1 + 20*x2 >= 91',
        '20*x2 + 12*x3 >= 49',
        '1*x1 + 16*x4 >= 82',
        '20*x2 + 16*x4 >= 69',
        '1*x1 + 20*x2 + 12*x3 + 16*x4 >= 69',
        '1*x2 - 5*x4 >= 0',
        '4*x1 - 4*x4 >= 0',
        '9*x1 - 7*x3 + 7*x4 >= 0',
        '1*x1 + 16*x4 <= 147',
        '1*x1 + 20*x2 <= 275',
        '12*x3 + 16*x4 <= 378',
        '1*x1 + 20*x2 + 12*x3 <= 228'
    ]
}
```

## Step 6: Write the Gurobi code for the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="x1", lb=0)  # milligrams of vitamin K
    x2 = model.addVar(name="x2", lb=0)  # milligrams of vitamin B3
    x3 = model.addVar(name="x3", lb=0)  # milligrams of vitamin E
    x4 = model.addVar(name="x4", lb=0)  # milligrams of vitamin B12

    # Define the objective function
    model.setObjective(5 * x1 + 1 * x2 + 9 * x3 + 1 * x4, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(x1 + 20 * x2 >= 91)
    model.addConstr(20 * x2 + 12 * x3 >= 49)
    model.addConstr(x1 + 16 * x4 >= 82)
    model.addConstr(20 * x2 + 16 * x4 >= 69)
    model.addConstr(x1 + 20 * x2 + 12 * x3 + 16 * x4 >= 69)
    model.addConstr(x2 - 5 * x4 >= 0)
    model.addConstr(4 * x1 - 4 * x4 >= 0)
    model.addConstr(9 * x1 - 7 * x3 + 7 * x4 >= 0)
    model.addConstr(x1 + 16 * x4 <= 147)
    model.addConstr(x1 + 20 * x2 <= 275)
    model.addConstr(12 * x3 + 16 * x4 <= 378)
    model.addConstr(x1 + 20 * x2 + 12 * x3 <= 228)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin K: {x1.varValue}")
        print(f"Milligrams of vitamin B3: {x2.varValue}")
        print(f"Milligrams of vitamin E: {x3.varValue}")
        print(f"Milligrams of vitamin B12: {x4.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```