## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to minimize the cost of vitamin supplements while meeting the requirements for vitamin B and vitamin D.

Let's define the decision variables:
- $x$: the number of servings of gummy vitamins
- $y$: the number of servings of powder vitamins

The objective function to minimize is the total cost:
\[ \text{Minimize:} \quad 1x + 3y \]

Subject to the constraints:
1. Vitamin B requirement: $2x + 6y \geq 14$
2. Vitamin D requirement: $7x + 2y \geq 24$
3. Non-negativity constraints: $x \geq 0, y \geq 0$

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    x = model.addVar(name="gummy_vitamins", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    y = model.addVar(name="powder_vitamins", lb=0, vtype=gurobi.GRB.CONTINUOUS)

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

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

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x = {x.varValue}, y = {y.varValue}")
        print(f"Minimum cost: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_vitamin_supplement_problem()
```