## Step 1: Define the symbolic representation of the problem
Let's denote the number of servings of protein drink as $x_1$ and the number of servings of fruit snack as $x_2$. The objective is to minimize the total cost, which is $4x_1 + 12x_2$. The constraints are:
- Vitamin A: $45x_1 + 400x_2 \geq 100$
- Vitamin C: $200x_1 + 600x_2 \geq 500$
- Proteins: $300x_1 + 200x_2 \geq 3000$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## 2: Convert the problem into a symbolic representation
The symbolic representation can be written as:
```json
{
    'sym_variables': [('x1', 'protein drink servings'), ('x2', 'fruit snack servings')],
    'objective_function': '4*x1 + 12*x2',
    'constraints': [
        '45*x1 + 400*x2 >= 100',
        '200*x1 + 600*x2 >= 500',
        '300*x1 + 200*x2 >= 3000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 3: Translate the problem into Gurobi code
Now, let's translate this into Gurobi code in Python:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="protein_drink", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="fruit_snack", lb=0, ub=gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(4 * x1 + 12 * x2, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(45 * x1 + 400 * x2 >= 100, name="vitamin_A")
    model.addConstr(200 * x1 + 600 * x2 >= 500, name="vitamin_C")
    model.addConstr(300 * x1 + 200 * x2 >= 3000, name="proteins")

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Protein drink servings: {x1.varValue}")
        print(f"Fruit snack servings: {x2.varValue}")
        print(f"Total cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_diet_problem()
```