## Step 1: Define the symbolic representation of the problem
The problem involves variables: ['grams of fat', 'milligrams of vitamin B2', 'milligrams of vitamin B3']. Let's denote them as $x_1$, $x_2$, and $x_3$ respectively. The objective function to minimize is $9x_1 + 4x_2 + 2x_3$. The constraints are:
- $3.84x_1 \leq 60$
- $4.56x_2 \leq 60$
- $5.67x_3 \leq 60$
- $3.84x_1 + 5.67x_3 \geq 19$
- $3.84x_1 + 4.56x_2 \geq 16$
- $3.84x_1 + 4.56x_2 + 5.67x_3 \geq 16$
- $3x_2 - 2x_3 \geq 0$
- $x_1$ is continuous
- $x_2$ is an integer
- $x_3$ is continuous

## 2: Convert the problem into a symbolic representation
The symbolic variables are:
- $x_1$ for 'grams of fat'
- $x_2$ for 'milligrams of vitamin B2'
- $x_3$ for 'milligrams of vitamin B3'

The objective function is: $9x_1 + 4x_2 + 2x_3$

The constraints are:
- $3.84x_1 \leq 60$
- $4.56x_2 \leq 60$
- $5.67x_3 \leq 60$
- $3.84x_1 + 5.67x_3 \geq 19$
- $3.84x_1 + 4.56x_2 \geq 16$
- $3.84x_1 + 4.56x_2 + 5.67x_3 \geq 16$
- $3x_2 - 2x_3 \geq 0$

## 3: Express the problem in the required JSON format
```json
{
    'sym_variables': [
        ('x1', 'grams of fat'), 
        ('x2', 'milligrams of vitamin B2'), 
        ('x3', 'milligrams of vitamin B3')
    ], 
    'objective_function': '9*x1 + 4*x2 + 2*x3', 
    'constraints': [
        '3.84*x1 <= 60', 
        '4.56*x2 <= 60', 
        '5.67*x3 <= 60', 
        '3.84*x1 + 5.67*x3 >= 19', 
        '3.84*x1 + 4.56*x2 >= 16', 
        '3.84*x1 + 4.56*x2 + 5.67*x3 >= 16', 
        '3*x2 - 2*x3 >= 0'
    ]
}
```

## 4: Implement the problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="x1", lb=-float('inf'), ub=float('inf'))  # grams of fat
    x2 = model.addVar(name="x2", lb=0, ub=float('inf'), vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B2
    x3 = model.addVar(name="x3", lb=-float('inf'), ub=float('inf'))  # milligrams of vitamin B3

    # Define the objective function
    model.setObjective(9 * x1 + 4 * x2 + 2 * x3, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(3.84 * x1 <= 60)
    model.addConstr(4.56 * x2 <= 60)
    model.addConstr(5.67 * x3 <= 60)
    model.addConstr(3.84 * x1 + 5.67 * x3 >= 19)
    model.addConstr(3.84 * x1 + 4.56 * x2 >= 16)
    model.addConstr(3.84 * x1 + 4.56 * x2 + 5.67 * x3 >= 16)
    model.addConstr(3 * x2 - 2 * x3 >= 0)

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Grams of fat: {x1.varValue}")
        print(f"Milligrams of vitamin B2: {x2.varValue}")
        print(f"Milligrams of vitamin B3: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_optimization_problem()
```