## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the number of servings of gummy vitamins
- $x_2$ as the number of servings of powder vitamins

The objective is to minimize the cost, which is $1x_1 + 3x_2$.

## Step 2: Define the constraints based on the problem description

The constraints are:
- Vitamin B requirement: $2x_1 + 6x_2 \geq 14$
- Vitamin D requirement: $7x_1 + 2x_2 \geq 24$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Step 3: Express the problem in the required symbolic format

```json
{
    'sym_variables': [('x1', 'gummy vitamins'), ('x2', 'powder vitamins')],
    'objective_function': '1*x1 + 3*x2',
    'constraints': [
        '2*x1 + 6*x2 >= 14',
        '7*x1 + 2*x2 >= 24',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 4: Convert the problem into Gurobi code

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="gummy_vitamins")
    x2 = model.addVar(lb=0, name="powder_vitamins")

    # Define the objective function
    model.setObjective(1*x1 + 3*x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(2*x1 + 6*x2 >= 14, name="vitamin_B_requirement")
    model.addConstr(7*x1 + 2*x2 >= 24, name="vitamin_D_requirement")

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of gummy vitamins: {x1.varValue}")
        print(f"Number of powder vitamins: {x2.varValue}")
        print(f"Total cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_vitamin_problem()
```