To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of servings of gummy vitamins taken.
- $x_2$ as the number of servings of powder vitamins taken.

The objective is to minimize the total cost, which can be represented by the objective function:
\[ \text{Minimize} \quad 1x_1 + 3x_2 \]

Given the constraints:

1. The man needs at least 14 units of vitamin B: $2x_1 + 6x_2 \geq 14$.
2. The man needs at least 24 units of vitamin D: $7x_1 + 2x_2 \geq 24$.

Additionally, since the number of servings cannot be negative:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

Thus, the symbolic representation of the problem is:

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

This problem can be solved using Gurobi in Python. Here's how you could implement it:

```python
from gurobipy import *

# Create a new model
m = Model("Vitamin_Optimization")

# Add variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="gummy_vitamins")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="powder_vitamins")

# Set the objective function
m.setObjective(1*x1 + 3*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x1 + 6*x2 >= 14, "vitamin_b")
m.addConstr(7*x1 + 2*x2 >= 24, "vitamin_d")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of gummy vitamins: {x1.x}")
    print(f"Number of powder vitamins: {x2.x}")
    print(f"Total cost: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```